Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001248
Mapping
St001248: Integer partitions ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1]
 => 0
[2]
 => 2
[1,1]
 => 0
[3]
 => 0
[2,1]
 => 2
[1,1,1]
 => 0
[4]
 => 4
[3,1]
 => 0
[2,2]
 => 4
[2,1,1]
 => 2
[1,1,1,1]
 => 0
[5]
 => 0
[4,1]
 => 4
[3,2]
 => 2
[3,1,1]
 => 0
[2,2,1]
 => 4
[2,1,1,1]
 => 2
[1,1,1,1,1]
 => 0
[6]
 => 6
[5,1]
 => 0
[4,2]
 => 6
[4,1,1]
 => 4
[3,3]
 => 0
[3,2,1]
 => 2
[3,1,1,1]
 => 0
[2,2,2]
 => 6
[2,2,1,1]
 => 4
[2,1,1,1,1]
 => 2
[1,1,1,1,1,1]
 => 0
[7]
 => 0
[6,1]
 => 6
[5,2]
 => 2
[5,1,1]
 => 0
[4,3]
 => 4
[4,2,1]
 => 6
[4,1,1,1]
 => 4
[3,3,1]
 => 0
[3,2,2]
 => 4
[3,2,1,1]
 => 2
[3,1,1,1,1]
 => 0
[2,2,2,1]
 => 6
[2,2,1,1,1]
 => 4
[2,1,1,1,1,1]
 => 2
[1,1,1,1,1,1,1]
 => 0
[8]
 => 8
[7,1]
 => 0
[6,2]
 => 8
[6,1,1]
 => 6
[5,3]
 => 0
[5,2,1]
 => 2
Description
Sum of the even parts of a partition.
Matching statistic: St000422
(load all 6 compositions to match this statistic)
Mapping
Mp00043: Integer partitions —to Dyck path⟶ Dyck paths
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St000422: Graphs ⟶ ℤResult quality: 13% ●values known / values provided: 13%●distinct values known / distinct values provided: 56%
Values
[1]
 => [1,0,1,0]
 => [1,1] => ([(0,1)],2)
 => 2 = 0 + 2
[2]
 => [1,1,0,0,1,0]
 => [2,1] => ([(0,2),(1,2)],3)
 => ? = 2 + 2
[1,1]
 => [1,0,1,1,0,0]
 => [1,2] => ([(1,2)],3)
 => 2 = 0 + 2
[3]
 => [1,1,1,0,0,0,1,0]
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? = 0 + 2
[2,1]
 => [1,0,1,0,1,0]
 => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 4 = 2 + 2
[1,1,1]
 => [1,0,1,1,1,0,0,0]
 => [1,3] => ([(2,3)],4)
 => 2 = 0 + 2
[4]
 => [1,1,1,1,0,0,0,0,1,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
[3,1]
 => [1,1,0,1,0,0,1,0]
 => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => ? ∊ {4,4} + 2
[2,2]
 => [1,1,0,0,1,1,0,0]
 => [2,2] => ([(1,3),(2,3)],4)
 => ? ∊ {4,4} + 2
[2,1,1]
 => [1,0,1,1,0,1,0,0]
 => [1,3] => ([(2,3)],4)
 => 2 = 0 + 2
[1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0]
 => [1,4] => ([(3,4)],5)
 => 2 = 0 + 2
[5]
 => [1,1,1,1,1,0,0,0,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? ∊ {0,4,4} + 2
[4,1]
 => [1,1,1,0,1,0,0,0,1,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
[3,2]
 => [1,1,0,0,1,0,1,0]
 => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,4,4} + 2
[3,1,1]
 => [1,0,1,1,0,0,1,0]
 => [1,2,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => ? ∊ {0,4,4} + 2
[2,2,1]
 => [1,0,1,0,1,1,0,0]
 => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 4 = 2 + 2
[2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,0]
 => [1,4] => ([(3,4)],5)
 => 2 = 0 + 2
[1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,0]
 => [1,5] => ([(4,5)],6)
 => 2 = 0 + 2
[6]
 => [1,1,1,1,1,1,0,0,0,0,0,0,1,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? ∊ {4,6,6,6} + 2
[5,1]
 => [1,1,1,1,0,1,0,0,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? ∊ {4,6,6,6} + 2
[4,2]
 => [1,1,1,0,0,1,0,0,1,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
[4,1,1]
 => [1,1,0,1,1,0,0,0,1,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
[3,3]
 => [1,1,1,0,0,0,1,1,0,0]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {4,6,6,6} + 2
[3,2,1]
 => [1,0,1,0,1,0,1,0]
 => [1,1,1,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 6 = 4 + 2
[3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,0]
 => [1,4] => ([(3,4)],5)
 => 2 = 0 + 2
[2,2,2]
 => [1,1,0,0,1,1,1,0,0,0]
 => [2,3] => ([(2,4),(3,4)],5)
 => ? ∊ {4,6,6,6} + 2
[2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,0]
 => [1,4] => ([(3,4)],5)
 => 2 = 0 + 2
[2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,0,0]
 => [1,5] => ([(4,5)],6)
 => 2 = 0 + 2
[1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,0,0,0,0,0]
 => [1,6] => ([(5,6)],7)
 => 2 = 0 + 2
[7]
 => [1,1,1,1,1,1,1,0,0,0,0,0,0,0,1,0]
 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? ∊ {0,2,4,4,4,6,6,6} + 2
[6,1]
 => [1,1,1,1,1,0,1,0,0,0,0,0,1,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? ∊ {0,2,4,4,4,6,6,6} + 2
[5,2]
 => [1,1,1,1,0,0,1,0,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? ∊ {0,2,4,4,4,6,6,6} + 2
[5,1,1]
 => [1,1,1,0,1,1,0,0,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? ∊ {0,2,4,4,4,6,6,6} + 2
[4,3]
 => [1,1,1,0,0,0,1,0,1,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6 = 4 + 2
[4,2,1]
 => [1,1,0,1,0,1,0,0,1,0]
 => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 4 = 2 + 2
[4,1,1,1]
 => [1,0,1,1,1,0,0,0,1,0]
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {0,2,4,4,4,6,6,6} + 2
[3,3,1]
 => [1,1,0,1,0,0,1,1,0,0]
 => [3,2] => ([(1,4),(2,4),(3,4)],5)
 => ? ∊ {0,2,4,4,4,6,6,6} + 2
[3,2,2]
 => [1,1,0,0,1,1,0,1,0,0]
 => [2,3] => ([(2,4),(3,4)],5)
 => ? ∊ {0,2,4,4,4,6,6,6} + 2
[3,2,1,1]
 => [1,0,1,1,0,1,0,1,0,0]
 => [1,4] => ([(3,4)],5)
 => 2 = 0 + 2
[3,1,1,1,1]
 => [1,0,1,1,1,1,0,0,1,0,0,0]
 => [1,5] => ([(4,5)],6)
 => 2 = 0 + 2
[2,2,2,1]
 => [1,0,1,0,1,1,1,0,0,0]
 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
[2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,0,0,0,0]
 => [1,5] => ([(4,5)],6)
 => 2 = 0 + 2
[2,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,1,0,0,0,0,0]
 => [1,6] => ([(5,6)],7)
 => 2 = 0 + 2
[1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,0,0,0,0,0,0,0]
 => [1,7] => ([(6,7)],8)
 => ? ∊ {0,2,4,4,4,6,6,6} + 2
[8]
 => [1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,1,0]
 => [8,1] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ? ∊ {0,2,2,4,4,4,6,6,6,8,8,8,8,8} + 2
[7,1]
 => [1,1,1,1,1,1,0,1,0,0,0,0,0,0,1,0]
 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? ∊ {0,2,2,4,4,4,6,6,6,8,8,8,8,8} + 2
[6,2]
 => [1,1,1,1,1,0,0,1,0,0,0,0,1,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? ∊ {0,2,2,4,4,4,6,6,6,8,8,8,8,8} + 2
[6,1,1]
 => [1,1,1,1,0,1,1,0,0,0,0,0,1,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? ∊ {0,2,2,4,4,4,6,6,6,8,8,8,8,8} + 2
[5,3]
 => [1,1,1,1,0,0,0,1,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? ∊ {0,2,2,4,4,4,6,6,6,8,8,8,8,8} + 2
[5,2,1]
 => [1,1,1,0,1,0,1,0,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? ∊ {0,2,2,4,4,4,6,6,6,8,8,8,8,8} + 2
[5,1,1,1]
 => [1,1,0,1,1,1,0,0,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? ∊ {0,2,2,4,4,4,6,6,6,8,8,8,8,8} + 2
[4,4]
 => [1,1,1,1,0,0,0,0,1,1,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 4 = 2 + 2
[4,3,1]
 => [1,1,0,1,0,0,1,0,1,0]
 => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6 = 4 + 2
[4,2,2]
 => [1,1,0,0,1,1,0,0,1,0]
 => [2,2,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {0,2,2,4,4,4,6,6,6,8,8,8,8,8} + 2
[4,2,1,1]
 => [1,0,1,1,0,1,0,0,1,0]
 => [1,3,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {0,2,2,4,4,4,6,6,6,8,8,8,8,8} + 2
[4,1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,1,0,0]
 => [1,5] => ([(4,5)],6)
 => 2 = 0 + 2
[3,3,2]
 => [1,1,0,0,1,0,1,1,0,0]
 => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {0,2,2,4,4,4,6,6,6,8,8,8,8,8} + 2
[3,3,1,1]
 => [1,0,1,1,0,0,1,1,0,0]
 => [1,2,2] => ([(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {0,2,2,4,4,4,6,6,6,8,8,8,8,8} + 2
[3,2,2,1]
 => [1,0,1,0,1,1,0,1,0,0]
 => [1,1,3] => ([(2,3),(2,4),(3,4)],5)
 => 4 = 2 + 2
[3,2,1,1,1]
 => [1,0,1,1,1,0,1,0,1,0,0,0]
 => [1,5] => ([(4,5)],6)
 => 2 = 0 + 2
[3,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,1,0,0,0,0]
 => [1,6] => ([(5,6)],7)
 => 2 = 0 + 2
[2,2,2,2]
 => [1,1,0,0,1,1,1,1,0,0,0,0]
 => [2,4] => ([(3,5),(4,5)],6)
 => ? ∊ {0,2,2,4,4,4,6,6,6,8,8,8,8,8} + 2
[2,2,2,1,1]
 => [1,0,1,1,0,1,1,1,0,0,0,0]
 => [1,5] => ([(4,5)],6)
 => 2 = 0 + 2
[2,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,1,0,0,0,0,0]
 => [1,6] => ([(5,6)],7)
 => 2 = 0 + 2
[2,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,0,1,0,0,0,0,0,0]
 => [1,7] => ([(6,7)],8)
 => ? ∊ {0,2,2,4,4,4,6,6,6,8,8,8,8,8} + 2
[1,1,1,1,1,1,1,1]
 => [1,0,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0]
 => [1,8] => ([(7,8)],9)
 => ? ∊ {0,2,2,4,4,4,6,6,6,8,8,8,8,8} + 2
[9]
 => [1,1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0,1,0]
 => [9,1] => ([(0,9),(1,9),(2,9),(3,9),(4,9),(5,9),(6,9),(7,9),(8,9)],10)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[8,1]
 => [1,1,1,1,1,1,1,0,1,0,0,0,0,0,0,0,1,0]
 => [8,1] => ([(0,8),(1,8),(2,8),(3,8),(4,8),(5,8),(6,8),(7,8)],9)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[7,2]
 => [1,1,1,1,1,1,0,0,1,0,0,0,0,0,1,0]
 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[7,1,1]
 => [1,1,1,1,1,0,1,1,0,0,0,0,0,0,1,0]
 => [7,1] => ([(0,7),(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[6,3]
 => [1,1,1,1,1,0,0,0,1,0,0,0,1,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[6,2,1]
 => [1,1,1,1,0,1,0,1,0,0,0,0,1,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[6,1,1,1]
 => [1,1,1,0,1,1,1,0,0,0,0,0,1,0]
 => [6,1] => ([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[5,4]
 => [1,1,1,1,0,0,0,0,1,0,1,0]
 => [4,1,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[5,3,1]
 => [1,1,1,0,1,0,0,1,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[5,2,2]
 => [1,1,1,0,0,1,1,0,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[5,2,1,1]
 => [1,1,0,1,1,0,1,0,0,0,1,0]
 => [5,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[5,1,1,1,1]
 => [1,0,1,1,1,1,0,0,0,0,1,0]
 => [1,4,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[4,4,1]
 => [1,1,1,0,1,0,0,0,1,1,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 4 = 2 + 2
[4,3,2]
 => [1,1,0,0,1,0,1,0,1,0]
 => [2,1,1,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[4,3,1,1]
 => [1,0,1,1,0,0,1,0,1,0]
 => [1,2,1,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[4,2,2,1]
 => [1,0,1,0,1,1,0,0,1,0]
 => [1,1,2,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[4,2,1,1,1]
 => [1,0,1,1,1,0,1,0,0,1,0,0]
 => [1,5] => ([(4,5)],6)
 => 2 = 0 + 2
[4,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,1,0,0,0]
 => [1,6] => ([(5,6)],7)
 => 2 = 0 + 2
[3,3,3]
 => [1,1,1,0,0,0,1,1,1,0,0,0]
 => [3,3] => ([(2,5),(3,5),(4,5)],6)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[3,3,2,1]
 => [1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,2] => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 6 = 4 + 2
[3,3,1,1,1]
 => [1,0,1,1,1,0,0,1,1,0,0,0]
 => [1,5] => ([(4,5)],6)
 => 2 = 0 + 2
[3,2,2,2]
 => [1,1,0,0,1,1,1,0,1,0,0,0]
 => [2,4] => ([(3,5),(4,5)],6)
 => ? ∊ {0,0,2,2,2,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8} + 2
[3,2,2,1,1]
 => [1,0,1,1,0,1,1,0,1,0,0,0]
 => [1,5] => ([(4,5)],6)
 => 2 = 0 + 2
[3,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,1,0,0,0,0]
 => [1,6] => ([(5,6)],7)
 => 2 = 0 + 2
[2,2,2,2,1]
 => [1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,1,4] => ([(3,4),(3,5),(4,5)],6)
 => 4 = 2 + 2
[2,2,2,1,1,1]
 => [1,0,1,1,1,0,1,1,1,0,0,0,0,0]
 => [1,6] => ([(5,6)],7)
 => 2 = 0 + 2
[5,1,1,1,1,1]
 => [1,0,1,1,1,1,1,0,0,0,0,1,0,0]
 => [1,6] => ([(5,6)],7)
 => 2 = 0 + 2
[4,4,2]
 => [1,1,1,0,0,1,0,0,1,1,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 4 = 2 + 2
[4,4,1,1]
 => [1,1,0,1,1,0,0,0,1,1,0,0]
 => [4,2] => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 4 = 2 + 2
[4,3,2,1]
 => [1,0,1,0,1,0,1,0,1,0]
 => [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)
 => 8 = 6 + 2
[4,3,1,1,1]
 => [1,0,1,1,1,0,0,1,0,1,0,0]
 => [1,5] => ([(4,5)],6)
 => 2 = 0 + 2
[4,2,2,1,1]
 => [1,0,1,1,0,1,1,0,0,1,0,0]
 => [1,5] => ([(4,5)],6)
 => 2 = 0 + 2
[4,2,1,1,1,1]
 => [1,0,1,1,1,1,0,1,0,0,1,0,0,0]
 => [1,6] => ([(5,6)],7)
 => 2 = 0 + 2
[3,3,2,1,1]
 => [1,0,1,1,0,1,0,1,1,0,0,0]
 => [1,5] => ([(4,5)],6)
 => 2 = 0 + 2
Description
The energy of a graph, if it is integral. The energy of a graph is the sum of the absolute values of its eigenvalues. This statistic is only defined for graphs with integral energy. It is known, that the energy is never an odd integer [2]. In fact, it is never the square root of an odd integer [3]. The energy of a graph is the sum of the energies of the connected components of a graph. The energy of the complete graph $K_n$ equals $2n-2$. For this reason, we do not define the energy of the empty graph.