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Your data matches 49 different statistics following compositions of up to 3 maps.
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Matching statistic: St001195
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
St001195: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Mp00231: Integer compositions —bounce path⟶ Dyck paths
Mp00122: Dyck paths —Elizalde-Deutsch bijection⟶ Dyck paths
St001195: Dyck paths ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
000 => [3] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 0
001 => [2,1] => [1,1,0,0,1,0]
=> [1,1,1,0,0,0]
=> 1
010 => [1,1,1] => [1,0,1,0,1,0]
=> [1,1,0,0,1,0]
=> 0
011 => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 1
100 => [1,2] => [1,0,1,1,0,0]
=> [1,1,0,1,0,0]
=> 1
101 => [1,1,1] => [1,0,1,0,1,0]
=> [1,1,0,0,1,0]
=> 0
110 => [2,1] => [1,1,0,0,1,0]
=> [1,1,1,0,0,0]
=> 1
111 => [3] => [1,1,1,0,0,0]
=> [1,0,1,0,1,0]
=> 0
0000 => [4] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 0
0001 => [3,1] => [1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,0]
=> 1
0010 => [2,1,1] => [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 1
0011 => [2,2] => [1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0]
=> 1
0100 => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> 1
0101 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> 1
0110 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> 0
0111 => [1,3] => [1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> 1
1000 => [1,3] => [1,0,1,1,1,0,0,0]
=> [1,1,0,1,0,1,0,0]
=> 1
1001 => [1,2,1] => [1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,0,1,0]
=> 0
1010 => [1,1,1,1] => [1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,0]
=> 1
1011 => [1,1,2] => [1,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0]
=> 1
1100 => [2,2] => [1,1,0,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0]
=> 1
1101 => [2,1,1] => [1,1,0,0,1,0,1,0]
=> [1,1,1,0,0,1,0,0]
=> 1
1110 => [3,1] => [1,1,1,0,0,0,1,0]
=> [1,1,1,0,1,0,0,0]
=> 1
1111 => [4] => [1,1,1,1,0,0,0,0]
=> [1,0,1,0,1,0,1,0]
=> 0
00000 => [5] => [1,1,1,1,1,0,0,0,0,0]
=> [1,0,1,0,1,0,1,0,1,0]
=> 0
00001 => [4,1] => [1,1,1,1,0,0,0,0,1,0]
=> [1,1,1,0,1,0,1,0,0,0]
=> 1
00010 => [3,1,1] => [1,1,1,0,0,0,1,0,1,0]
=> [1,1,1,0,1,1,0,0,0,0]
=> 1
00011 => [3,2] => [1,1,1,0,0,0,1,1,0,0]
=> [1,1,1,1,1,0,0,0,0,0]
=> 1
00100 => [2,1,2] => [1,1,0,0,1,0,1,1,0,0]
=> [1,1,1,1,0,0,0,0,1,0]
=> 1
00101 => [2,1,1,1] => [1,1,0,0,1,0,1,0,1,0]
=> [1,1,1,0,0,1,0,0,1,0]
=> 0
00110 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> 1
00111 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1
01000 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 1
01001 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> 1
01010 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 0
01011 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> 1
01100 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> 1
01101 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 1
01110 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 0
01111 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1
10000 => [1,4] => [1,0,1,1,1,1,0,0,0,0]
=> [1,1,0,1,0,1,0,1,0,0]
=> 1
10001 => [1,3,1] => [1,0,1,1,1,0,0,0,1,0]
=> [1,1,0,0,1,0,1,0,1,0]
=> 0
10010 => [1,2,1,1] => [1,0,1,1,0,0,1,0,1,0]
=> [1,1,0,0,1,1,1,0,0,0]
=> 1
10011 => [1,2,2] => [1,0,1,1,0,0,1,1,0,0]
=> [1,1,0,1,1,0,1,0,0,0]
=> 1
10100 => [1,1,1,2] => [1,0,1,0,1,0,1,1,0,0]
=> [1,1,0,1,1,0,0,0,1,0]
=> 1
10101 => [1,1,1,1,1] => [1,0,1,0,1,0,1,0,1,0]
=> [1,1,0,0,1,1,0,0,1,0]
=> 0
10110 => [1,1,2,1] => [1,0,1,0,1,1,0,0,1,0]
=> [1,1,0,0,1,1,0,1,0,0]
=> 1
10111 => [1,1,3] => [1,0,1,0,1,1,1,0,0,0]
=> [1,1,0,1,1,1,0,0,0,0]
=> 1
11000 => [2,3] => [1,1,0,0,1,1,1,0,0,0]
=> [1,1,1,1,0,1,0,0,0,0]
=> 1
11001 => [2,2,1] => [1,1,0,0,1,1,0,0,1,0]
=> [1,1,1,0,0,1,0,1,0,0]
=> 1
Description
The global dimension of the algebra $A/AfA$ of the corresponding Nakayama algebra $A$ with minimal left faithful projective-injective module $Af$.
Matching statistic: St000259
Mp00097: Binary words —delta morphism⟶ Integer compositions
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 100%
Mp00039: Integer compositions —complement⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000259: Graphs ⟶ ℤResult quality: 50% ●values known / values provided: 50%●distinct values known / distinct values provided: 100%
Values
000 => [3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 1 = 0 + 1
001 => [2,1] => [1,2] => ([(1,2)],3)
=> ? = 1 + 1
010 => [1,1,1] => [3] => ([],3)
=> ? = 0 + 1
011 => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 1 + 1
100 => [1,2] => [2,1] => ([(0,2),(1,2)],3)
=> 2 = 1 + 1
101 => [1,1,1] => [3] => ([],3)
=> ? = 0 + 1
110 => [2,1] => [1,2] => ([(1,2)],3)
=> ? = 1 + 1
111 => [3] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
=> 1 = 0 + 1
0000 => [4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
0001 => [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 1 + 1
0010 => [2,1,1] => [1,3] => ([(2,3)],4)
=> ? = 1 + 1
0011 => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
0100 => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 1 + 1
0101 => [1,1,1,1] => [4] => ([],4)
=> ? = 1 + 1
0110 => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
0111 => [1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
1000 => [1,3] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
1001 => [1,2,1] => [2,2] => ([(1,3),(2,3)],4)
=> ? = 0 + 1
1010 => [1,1,1,1] => [4] => ([],4)
=> ? = 1 + 1
1011 => [1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
=> 2 = 1 + 1
1100 => [2,2] => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
=> 2 = 1 + 1
1101 => [2,1,1] => [1,3] => ([(2,3)],4)
=> ? = 1 + 1
1110 => [3,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
=> ? = 1 + 1
1111 => [4] => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
=> 1 = 0 + 1
00000 => [5] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
00001 => [4,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
00010 => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
00011 => [3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
00100 => [2,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
00101 => [2,1,1,1] => [1,4] => ([(3,4)],5)
=> ? = 0 + 1
00110 => [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
00111 => [2,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
01000 => [1,1,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
01001 => [1,1,2,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 1
01010 => [1,1,1,1,1] => [5] => ([],5)
=> ? = 0 + 1
01011 => [1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
01100 => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
01101 => [1,2,1,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 1
01110 => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 1
01111 => [1,4] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
10000 => [1,4] => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
10001 => [1,3,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 0 + 1
10010 => [1,2,1,1] => [2,3] => ([(2,4),(3,4)],5)
=> ? = 1 + 1
10011 => [1,2,2] => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
10100 => [1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
=> 2 = 1 + 1
10101 => [1,1,1,1,1] => [5] => ([],5)
=> ? = 0 + 1
10110 => [1,1,2,1] => [3,2] => ([(1,4),(2,4),(3,4)],5)
=> ? = 1 + 1
10111 => [1,1,3] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
11000 => [2,3] => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
11001 => [2,2,1] => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
11010 => [2,1,1,1] => [1,4] => ([(3,4)],5)
=> ? = 0 + 1
11011 => [2,1,2] => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
11100 => [3,2] => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 2 = 1 + 1
11101 => [3,1,1] => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
11110 => [4,1] => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> ? = 1 + 1
11111 => [5] => [1,1,1,1,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
=> 1 = 0 + 1
Description
The diameter of a connected graph.
This is the greatest distance between any pair of vertices.
Matching statistic: St001095
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00262: Binary words —poset of factors⟶ Posets
St001095: Posets ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 100%
St001095: Posets ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 100%
Values
000 => ([(0,3),(2,1),(3,2)],4)
=> 0
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 0
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 0
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 1
111 => ([(0,3),(2,1),(3,2)],4)
=> 0
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ? = 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ? = 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ? = 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 0
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 0
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ? = 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ? = 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ? = 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 0
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ? = 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? = 0
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ? = 0
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? = 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 0
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 0
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? = 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ? = 0
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? = 0
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ? = 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 0
Description
The number of non-isomorphic posets with precisely one further covering relation.
Matching statistic: St001942
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Mp00262: Binary words —poset of factors⟶ Posets
St001942: Posets ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 100%
St001942: Posets ⟶ ℤResult quality: 21% ●values known / values provided: 21%●distinct values known / distinct values provided: 100%
Values
000 => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 1 + 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 1 = 0 + 1
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 1 + 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 1 + 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> 1 = 0 + 1
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> 2 = 1 + 1
111 => ([(0,3),(2,1),(3,2)],4)
=> 1 = 0 + 1
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 + 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ? = 1 + 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1 + 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ? = 1 + 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ? = 1 + 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 0 + 1
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 + 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 + 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ? = 0 + 1
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ? = 1 + 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ? = 1 + 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ? = 1 + 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ? = 1 + 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ? = 1 + 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> 1 = 0 + 1
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 0 + 1
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 1 + 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 1 + 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 1 + 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ? = 1 + 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? = 0 + 1
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 1 + 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 1 + 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 1 + 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 1 + 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ? = 0 + 1
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? = 1 + 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 1 + 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 1 + 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 0 + 1
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 1 + 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 1 + 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ? = 0 + 1
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 1 + 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 1 + 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? = 1 + 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ? = 0 + 1
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ? = 1 + 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 1 + 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 1 + 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ? = 1 + 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ? = 0 + 1
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ? = 1 + 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ? = 1 + 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ? = 1 + 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ? = 1 + 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> 1 = 0 + 1
Description
The number of loops of the quiver corresponding to the reduced incidence algebra of a poset.
Matching statistic: St000447
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
000 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 0
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 0
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
111 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? = 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? = 0
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? = 0
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? = 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? = 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 0
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? = 0
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? = 0
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? = 0
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? = 0
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 0
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? = 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0
Description
The number of pairs of vertices of a graph with distance 3.
This is the coefficient of the cubic term of the Wiener polynomial, also called Wiener polarity index.
Matching statistic: St001306
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
000 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 0
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 0
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
111 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? = 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? = 0
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? = 0
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? = 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? = 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 0
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? = 0
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? = 0
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? = 0
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? = 0
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 0
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? = 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0
Description
The number of induced paths on four vertices in a graph.
Matching statistic: St001350
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
000 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 0
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 0
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
111 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? = 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? = 0
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? = 0
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? = 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? = 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 0
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? = 0
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? = 0
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? = 0
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? = 0
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 0
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? = 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0
Description
Half of the Albertson index of a graph.
This is $\frac{1}{2}\sum_{\{u,v\}\in E}|d(u)-d(v)|$, where $E$ is the set of edges and $d_v$ is the degree of vertex $v$, see [1].
In particular, this statistic vanishes on graphs whose components are all regular, see [2].
Matching statistic: St001353
(load all 3 compositions to match this statistic)
(load all 3 compositions to match this statistic)
Values
000 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 0
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 0
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
111 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? = 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? = 0
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? = 0
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? = 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? = 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 0
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? = 0
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? = 0
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? = 0
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? = 0
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 0
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? = 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0
Description
The number of prime nodes in the modular decomposition of a graph.
Matching statistic: St001575
(load all 2 compositions to match this statistic)
(load all 2 compositions to match this statistic)
Values
000 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 0
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 0
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
111 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? = 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? = 0
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? = 0
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? = 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? = 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 0
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? = 0
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? = 0
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? = 0
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? = 0
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 0
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? = 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0
Description
The minimal number of edges to add or remove to make a graph edge transitive.
A graph is edge transitive, if for any two edges, there is an automorphism that maps one edge to the other.
Matching statistic: St001577
(load all 5 compositions to match this statistic)
(load all 5 compositions to match this statistic)
Values
000 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
001 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
010 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 0
011 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
100 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
101 => ([(0,1),(0,2),(1,4),(1,5),(2,4),(2,5),(4,3),(5,3)],6)
=> ([(2,5),(3,4)],6)
=> 0
110 => ([(0,2),(0,3),(1,5),(2,4),(3,1),(3,4),(4,5)],6)
=> ([(2,5),(3,4),(4,5)],6)
=> 1
111 => ([(0,3),(2,1),(3,2)],4)
=> ([],4)
=> 0
0000 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0
0001 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
0010 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
0011 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
0100 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
0101 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? = 1
0110 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? = 0
0111 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1000 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1001 => ([(0,2),(0,3),(1,5),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,6),(8,5)],9)
=> ([(2,5),(3,4),(3,7),(4,6),(5,8),(6,7),(6,8),(7,8)],9)
=> ? = 0
1010 => ([(0,1),(0,2),(1,6),(1,7),(2,6),(2,7),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5)],8)
=> ([(2,7),(3,6),(4,5)],8)
=> ? = 1
1011 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
1100 => ([(0,3),(0,4),(1,7),(2,6),(3,2),(3,5),(4,1),(4,5),(5,6),(5,7),(6,8),(7,8)],9)
=> ([(2,5),(2,8),(3,4),(3,8),(4,7),(5,7),(6,7),(6,8),(7,8)],9)
=> ? = 1
1101 => ([(0,2),(0,3),(1,6),(2,7),(2,8),(3,1),(3,7),(3,8),(5,4),(6,4),(7,5),(8,5),(8,6)],9)
=> ([(2,6),(3,4),(3,8),(4,7),(5,7),(5,8),(6,8),(7,8)],9)
=> ? = 1
1110 => ([(0,2),(0,4),(1,6),(2,5),(3,1),(3,7),(4,3),(4,5),(5,7),(7,6)],8)
=> ([(2,7),(3,6),(4,5),(4,6),(5,7),(6,7)],8)
=> ? = 1
1111 => ([(0,4),(2,3),(3,1),(4,2)],5)
=> ([],5)
=> 0
00000 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0
00001 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
00010 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
00011 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
00100 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? = 1
00101 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 0
00110 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
00111 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
01000 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
01001 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
01010 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? = 0
01011 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 1
01100 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
01101 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
01110 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? = 0
01111 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
10000 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
10001 => ([(0,3),(0,4),(1,2),(1,10),(1,11),(2,8),(2,9),(3,6),(3,7),(4,1),(4,6),(4,7),(6,11),(7,10),(8,5),(9,5),(10,8),(11,9)],12)
=> ([(2,6),(3,6),(3,9),(3,10),(4,5),(4,8),(4,10),(5,7),(5,9),(6,11),(7,8),(7,10),(7,11),(8,9),(8,11),(9,10),(9,11),(10,11)],12)
=> ? = 0
10010 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
10011 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
10100 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 1
10101 => ([(0,1),(0,2),(1,8),(1,9),(2,8),(2,9),(4,3),(5,3),(6,4),(6,5),(7,4),(7,5),(8,6),(8,7),(9,6),(9,7)],10)
=> ([(2,9),(3,8),(4,7),(5,6)],10)
=> ? = 0
10110 => ([(0,2),(0,3),(1,5),(1,9),(2,10),(2,11),(3,1),(3,10),(3,11),(5,7),(6,8),(7,4),(8,4),(9,7),(9,8),(10,5),(10,6),(11,6),(11,9)],12)
=> ([(2,5),(3,4),(3,11),(4,9),(5,10),(6,8),(6,9),(6,11),(7,8),(7,10),(7,11),(8,10),(9,10),(9,11)],12)
=> ? = 1
10111 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
11000 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
11001 => ([(0,3),(0,4),(1,9),(2,6),(2,11),(3,2),(3,10),(3,12),(4,1),(4,10),(4,12),(6,7),(7,5),(8,5),(9,8),(10,6),(11,7),(11,8),(12,9),(12,11)],13)
=> ([(2,3),(2,10),(3,12),(4,5),(4,8),(4,12),(5,9),(5,11),(6,8),(6,9),(6,11),(6,12),(7,9),(7,10),(7,11),(7,12),(8,9),(8,10),(8,11),(9,12),(10,11),(10,12),(11,12)],13)
=> ? = 1
11010 => ([(0,2),(0,3),(1,8),(2,10),(2,11),(3,1),(3,10),(3,11),(5,6),(6,4),(7,4),(8,7),(9,6),(9,7),(10,5),(10,9),(11,5),(11,8),(11,9)],12)
=> ([(2,5),(3,6),(3,11),(4,7),(4,9),(5,11),(6,10),(6,11),(7,10),(7,11),(8,9),(8,10),(8,11),(9,10),(9,11)],12)
=> ? = 0
11011 => ([(0,2),(0,3),(1,5),(1,6),(2,10),(2,11),(3,1),(3,10),(3,11),(5,8),(6,7),(7,4),(8,4),(9,7),(9,8),(10,6),(10,9),(11,5),(11,9)],12)
=> ([(2,5),(3,4),(3,10),(4,9),(5,11),(6,9),(6,10),(6,11),(7,8),(7,9),(7,11),(8,10),(8,11),(9,10)],12)
=> ? = 1
11100 => ([(0,4),(0,5),(1,9),(2,3),(2,11),(3,8),(4,1),(4,10),(5,2),(5,10),(7,6),(8,6),(9,7),(10,9),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(2,11),(3,6),(3,10),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,11),(7,9),(7,10),(8,9),(8,10),(9,11),(10,11)],12)
=> ? = 1
11101 => ([(0,3),(0,4),(1,2),(1,11),(2,8),(3,9),(3,10),(4,1),(4,9),(4,10),(6,7),(7,5),(8,5),(9,6),(10,6),(10,11),(11,7),(11,8)],12)
=> ([(2,7),(3,6),(3,11),(4,8),(4,10),(4,11),(5,9),(5,10),(5,11),(6,8),(6,10),(7,9),(7,11),(8,9),(8,11),(9,10),(10,11)],12)
=> ? = 1
11110 => ([(0,2),(0,5),(1,7),(2,6),(3,4),(3,9),(4,1),(4,8),(5,3),(5,6),(6,9),(8,7),(9,8)],10)
=> ([(2,9),(3,8),(4,7),(4,8),(5,6),(5,9),(6,7),(6,8),(7,9),(8,9)],10)
=> ? = 1
11111 => ([(0,5),(2,4),(3,2),(4,1),(5,3)],6)
=> ([],6)
=> 0
Description
The minimal number of edges to add or remove to make a graph a cograph.
A cograph is a graph that can be obtained from the one vertex graph by complementation and disjoint union.
The following 39 statistics, ordered by result quality, also match your data. Click on any of them to see the details.
St001723The differential of a graph. St001724The 2-packing differential of a graph. St001798The difference of the number of edges in a graph and the number of edges in the complement of the Turán graph. St000535The rank-width of a graph. St001111The weak 2-dynamic chromatic number of a graph. St001112The 3-weak dynamic number of a graph. St001646The number of edges that can be added without increasing the maximal degree of a graph. St001694The number of maximal dissociation sets in a graph. St001716The 1-improper chromatic number of a graph. St001774The degree of the minimal polynomial of the smallest eigenvalue of a graph. St001775The degree of the minimal polynomial of the largest eigenvalue of a graph. St001776The degree of the minimal polynomial of the largest Laplacian eigenvalue of a graph. St000172The Grundy number of a graph. St001581The achromatic number of a graph. St001647The number of edges that can be added without increasing the clique number. St001648The number of edges that can be added without increasing the chromatic number. St000985The number of positive eigenvalues of the adjacency matrix of the graph. St001282The number of graphs with the same chromatic polynomial. St001315The dissociation number of a graph. St001512The minimum rank of a graph. St001677The number of non-degenerate subsets of a lattice whose meet is the bottom element. St001845The number of join irreducibles minus the rank of a lattice. St001613The binary logarithm of the size of the center of a lattice. St001681The number of inclusion-wise minimal subsets of a lattice, whose meet is the bottom element. St001719The number of shortest chains of small intervals from the bottom to the top in a lattice. St001881The number of factors of a lattice as a Cartesian product of lattices. St001168The vector space dimension of the tilting module corresponding to the permutation in the Auslander algebra of $K[x]/(x^n)$. St001964The interval resolution global dimension of a poset. St001625The Möbius invariant of a lattice. St001877Number of indecomposable injective modules with projective dimension 2. St000741The Colin de Verdière graph invariant. St001118The acyclic chromatic index of a graph. St001621The number of atoms of a lattice. St001624The breadth of a lattice. St001630The global dimension of the incidence algebra of the lattice over the rational numbers. St001644The dimension of a graph. St001878The projective dimension of the simple modules corresponding to the minimum of L in the incidence algebra of the lattice L. St001330The hat guessing number of a graph. St000455The second largest eigenvalue of a graph if it is integral.
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