Your data matches 2 different statistics following compositions of up to 3 maps.
(click to perform a complete search on your data)
Matching statistic: St001281
Mapping
Mp00100: Dyck paths —touch composition⟶ Integer compositions
Mp00133: Integer compositions —delta morphism⟶ Integer compositions
Mp00184: Integer compositions —to threshold graph⟶ Graphs
St001281: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
[1,0,1,0]
 => [1,1] => [2] => ([],2)
 => 0
[1,0,1,0,1,0]
 => [1,1,1] => [3] => ([],3)
 => 0
[1,0,1,1,0,0]
 => [1,2] => [1,1] => ([(0,1)],2)
 => 1
[1,1,0,0,1,0]
 => [2,1] => [1,1] => ([(0,1)],2)
 => 1
[1,0,1,0,1,0,1,0]
 => [1,1,1,1] => [4] => ([],4)
 => 0
[1,0,1,0,1,1,0,0]
 => [1,1,2] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[1,0,1,1,0,0,1,0]
 => [1,2,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 2
[1,0,1,1,0,1,0,0]
 => [1,3] => [1,1] => ([(0,1)],2)
 => 1
[1,0,1,1,1,0,0,0]
 => [1,3] => [1,1] => ([(0,1)],2)
 => 1
[1,1,0,0,1,0,1,0]
 => [2,1,1] => [1,2] => ([(1,2)],3)
 => 0
[1,1,0,0,1,1,0,0]
 => [2,2] => [2] => ([],2)
 => 0
[1,1,0,1,0,0,1,0]
 => [3,1] => [1,1] => ([(0,1)],2)
 => 1
[1,1,1,0,0,0,1,0]
 => [3,1] => [1,1] => ([(0,1)],2)
 => 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1] => [5] => ([],5)
 => 0
[1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,2] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[1,0,1,0,1,1,0,0,1,0]
 => [1,1,2,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[1,0,1,0,1,1,0,1,0,0]
 => [1,1,3] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[1,0,1,0,1,1,1,0,0,0]
 => [1,1,3] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,2,1,1] => [1,1,2] => ([(1,2),(1,3),(2,3)],4)
 => 0
[1,0,1,1,0,0,1,1,0,0]
 => [1,2,2] => [1,2] => ([(1,2)],3)
 => 0
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 2
[1,0,1,1,0,1,0,1,0,0]
 => [1,4] => [1,1] => ([(0,1)],2)
 => 1
[1,0,1,1,0,1,1,0,0,0]
 => [1,4] => [1,1] => ([(0,1)],2)
 => 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,3,1] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 2
[1,0,1,1,1,0,0,1,0,0]
 => [1,4] => [1,1] => ([(0,1)],2)
 => 1
[1,0,1,1,1,0,1,0,0,0]
 => [1,4] => [1,1] => ([(0,1)],2)
 => 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,4] => [1,1] => ([(0,1)],2)
 => 1
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,1,1] => [1,3] => ([(2,3)],4)
 => 0
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,2] => [1,1,1] => ([(0,1),(0,2),(1,2)],3)
 => 2
[1,1,0,0,1,1,0,0,1,0]
 => [2,2,1] => [2,1] => ([(0,2),(1,2)],3)
 => 1
[1,1,0,0,1,1,0,1,0,0]
 => [2,3] => [1,1] => ([(0,1)],2)
 => 1
[1,1,0,0,1,1,1,0,0,0]
 => [2,3] => [1,1] => ([(0,1)],2)
 => 1
[1,1,0,1,0,0,1,0,1,0]
 => [3,1,1] => [1,2] => ([(1,2)],3)
 => 0
[1,1,0,1,0,0,1,1,0,0]
 => [3,2] => [1,1] => ([(0,1)],2)
 => 1
[1,1,0,1,0,1,0,0,1,0]
 => [4,1] => [1,1] => ([(0,1)],2)
 => 1
[1,1,0,1,1,0,0,0,1,0]
 => [4,1] => [1,1] => ([(0,1)],2)
 => 1
[1,1,1,0,0,0,1,0,1,0]
 => [3,1,1] => [1,2] => ([(1,2)],3)
 => 0
[1,1,1,0,0,0,1,1,0,0]
 => [3,2] => [1,1] => ([(0,1)],2)
 => 1
[1,1,1,0,0,1,0,0,1,0]
 => [4,1] => [1,1] => ([(0,1)],2)
 => 1
[1,1,1,0,1,0,0,0,1,0]
 => [4,1] => [1,1] => ([(0,1)],2)
 => 1
[1,1,1,1,0,0,0,0,1,0]
 => [4,1] => [1,1] => ([(0,1)],2)
 => 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,1,1,1,1,1] => [6] => ([],6)
 => 0
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,1,1,1,2] => [4,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 2
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,1,1,2,1] => [3,1,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 4
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,1,1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,1,1,3] => [3,1] => ([(0,3),(1,3),(2,3)],4)
 => 2
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,1,2,1,1] => [2,1,2] => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 0
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,1,2,2] => [2,2] => ([(1,3),(2,3)],4)
 => 0
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,1,3,1] => [2,1,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 3
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,1,4] => [2,1] => ([(0,2),(1,2)],3)
 => 1
Description
The normalized isoperimetric number of a graph. The isoperimetric number, or Cheeger constant, of a graph $G$ is $$ i(G) = \min\left\{\frac{|\partial A|}{|A|}\ : \ A\subseteq V(G), 0 < |A|\leq |V(G)|/2\right\}, $$ where $$ \partial A := \{(x, y)\in E(G)\ : \ x\in A, y\in V(G)\setminus A \}. $$ This statistic is $i(G)\cdot\lfloor n/2\rfloor$.
Matching statistic: St000260
(load all 2 compositions to match this statistic)
Mapping
Mp00031: Dyck paths —to 312-avoiding permutation⟶ Permutations
Mp00252: Permutations —restriction⟶ Permutations
Mp00160: Permutations —graph of inversions⟶ Graphs
St000260: Graphs ⟶ ℤResult quality: 2% ●values known / values provided: 2%●distinct values known / distinct values provided: 15%
Values
[1,0,1,0]
 => [1,2] => [1] => ([],1)
 => 0
[1,0,1,0,1,0]
 => [1,2,3] => [1,2] => ([],2)
 => ? = 0
[1,0,1,1,0,0]
 => [1,3,2] => [1,2] => ([],2)
 => ? = 1
[1,1,0,0,1,0]
 => [2,1,3] => [2,1] => ([(0,1)],2)
 => 1
[1,0,1,0,1,0,1,0]
 => [1,2,3,4] => [1,2,3] => ([],3)
 => ? = 0
[1,0,1,0,1,1,0,0]
 => [1,2,4,3] => [1,2,3] => ([],3)
 => ? = 1
[1,0,1,1,0,0,1,0]
 => [1,3,2,4] => [1,3,2] => ([(1,2)],3)
 => ? = 2
[1,0,1,1,0,1,0,0]
 => [1,3,4,2] => [1,3,2] => ([(1,2)],3)
 => ? = 1
[1,0,1,1,1,0,0,0]
 => [1,4,3,2] => [1,3,2] => ([(1,2)],3)
 => ? = 1
[1,1,0,0,1,0,1,0]
 => [2,1,3,4] => [2,1,3] => ([(1,2)],3)
 => ? = 0
[1,1,0,0,1,1,0,0]
 => [2,1,4,3] => [2,1,3] => ([(1,2)],3)
 => ? = 0
[1,1,0,1,0,0,1,0]
 => [2,3,1,4] => [2,3,1] => ([(0,2),(1,2)],3)
 => 1
[1,1,1,0,0,0,1,0]
 => [3,2,1,4] => [3,2,1] => ([(0,1),(0,2),(1,2)],3)
 => 1
[1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5] => [1,2,3,4] => ([],4)
 => ? = 0
[1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,5,4] => [1,2,3,4] => ([],4)
 => ? = 2
[1,0,1,0,1,1,0,0,1,0]
 => [1,2,4,3,5] => [1,2,4,3] => ([(2,3)],4)
 => ? = 3
[1,0,1,0,1,1,0,1,0,0]
 => [1,2,4,5,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 1
[1,0,1,0,1,1,1,0,0,0]
 => [1,2,5,4,3] => [1,2,4,3] => ([(2,3)],4)
 => ? = 1
[1,0,1,1,0,0,1,0,1,0]
 => [1,3,2,4,5] => [1,3,2,4] => ([(2,3)],4)
 => ? = 0
[1,0,1,1,0,0,1,1,0,0]
 => [1,3,2,5,4] => [1,3,2,4] => ([(2,3)],4)
 => ? = 0
[1,0,1,1,0,1,0,0,1,0]
 => [1,3,4,2,5] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 2
[1,0,1,1,0,1,0,1,0,0]
 => [1,3,4,5,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 1
[1,0,1,1,0,1,1,0,0,0]
 => [1,3,5,4,2] => [1,3,4,2] => ([(1,3),(2,3)],4)
 => ? = 1
[1,0,1,1,1,0,0,0,1,0]
 => [1,4,3,2,5] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 2
[1,0,1,1,1,0,0,1,0,0]
 => [1,4,3,5,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[1,0,1,1,1,0,1,0,0,0]
 => [1,4,5,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[1,0,1,1,1,1,0,0,0,0]
 => [1,5,4,3,2] => [1,4,3,2] => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[1,1,0,0,1,0,1,0,1,0]
 => [2,1,3,4,5] => [2,1,3,4] => ([(2,3)],4)
 => ? = 0
[1,1,0,0,1,0,1,1,0,0]
 => [2,1,3,5,4] => [2,1,3,4] => ([(2,3)],4)
 => ? = 2
[1,1,0,0,1,1,0,0,1,0]
 => [2,1,4,3,5] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 1
[1,1,0,0,1,1,0,1,0,0]
 => [2,1,4,5,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 1
[1,1,0,0,1,1,1,0,0,0]
 => [2,1,5,4,3] => [2,1,4,3] => ([(0,3),(1,2)],4)
 => ? = 1
[1,1,0,1,0,0,1,0,1,0]
 => [2,3,1,4,5] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 0
[1,1,0,1,0,0,1,1,0,0]
 => [2,3,1,5,4] => [2,3,1,4] => ([(1,3),(2,3)],4)
 => ? = 1
[1,1,0,1,0,1,0,0,1,0]
 => [2,3,4,1,5] => [2,3,4,1] => ([(0,3),(1,3),(2,3)],4)
 => 1
[1,1,0,1,1,0,0,0,1,0]
 => [2,4,3,1,5] => [2,4,3,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[1,1,1,0,0,0,1,0,1,0]
 => [3,2,1,4,5] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 0
[1,1,1,0,0,0,1,1,0,0]
 => [3,2,1,5,4] => [3,2,1,4] => ([(1,2),(1,3),(2,3)],4)
 => ? = 1
[1,1,1,0,0,1,0,0,1,0]
 => [3,2,4,1,5] => [3,2,4,1] => ([(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[1,1,1,0,1,0,0,0,1,0]
 => [3,4,2,1,5] => [3,4,2,1] => ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[1,1,1,1,0,0,0,0,1,0]
 => [4,3,2,1,5] => [4,3,2,1] => ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 1
[1,0,1,0,1,0,1,0,1,0,1,0]
 => [1,2,3,4,5,6] => [1,2,3,4,5] => ([],5)
 => ? = 0
[1,0,1,0,1,0,1,0,1,1,0,0]
 => [1,2,3,4,6,5] => [1,2,3,4,5] => ([],5)
 => ? = 2
[1,0,1,0,1,0,1,1,0,0,1,0]
 => [1,2,3,5,4,6] => [1,2,3,5,4] => ([(3,4)],5)
 => ? = 4
[1,0,1,0,1,0,1,1,0,1,0,0]
 => [1,2,3,5,6,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ? = 2
[1,0,1,0,1,0,1,1,1,0,0,0]
 => [1,2,3,6,5,4] => [1,2,3,5,4] => ([(3,4)],5)
 => ? = 2
[1,0,1,0,1,1,0,0,1,0,1,0]
 => [1,2,4,3,5,6] => [1,2,4,3,5] => ([(3,4)],5)
 => ? = 0
[1,0,1,0,1,1,0,0,1,1,0,0]
 => [1,2,4,3,6,5] => [1,2,4,3,5] => ([(3,4)],5)
 => ? = 0
[1,0,1,0,1,1,0,1,0,0,1,0]
 => [1,2,4,5,3,6] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ? = 3
[1,0,1,0,1,1,0,1,0,1,0,0]
 => [1,2,4,5,6,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ? = 1
[1,0,1,0,1,1,0,1,1,0,0,0]
 => [1,2,4,6,5,3] => [1,2,4,5,3] => ([(2,4),(3,4)],5)
 => ? = 1
[1,0,1,0,1,1,1,0,0,0,1,0]
 => [1,2,5,4,3,6] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ? = 3
[1,0,1,0,1,1,1,0,0,1,0,0]
 => [1,2,5,4,6,3] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ? = 1
[1,0,1,0,1,1,1,0,1,0,0,0]
 => [1,2,5,6,4,3] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ? = 1
[1,0,1,0,1,1,1,1,0,0,0,0]
 => [1,2,6,5,4,3] => [1,2,5,4,3] => ([(2,3),(2,4),(3,4)],5)
 => ? = 1
[1,0,1,1,0,0,1,0,1,0,1,0]
 => [1,3,2,4,5,6] => [1,3,2,4,5] => ([(3,4)],5)
 => ? = 0
[1,0,1,1,0,0,1,0,1,1,0,0]
 => [1,3,2,4,6,5] => [1,3,2,4,5] => ([(3,4)],5)
 => ? = 4
[1,0,1,1,0,0,1,1,0,0,1,0]
 => [1,3,2,5,4,6] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
 => ? = 2
[1,0,1,1,0,0,1,1,0,1,0,0]
 => [1,3,2,5,6,4] => [1,3,2,5,4] => ([(1,4),(2,3)],5)
 => ? = 2
[1,1,0,1,0,1,0,1,0,0,1,0]
 => [2,3,4,5,1,6] => [2,3,4,5,1] => ([(0,4),(1,4),(2,4),(3,4)],5)
 => 1
[1,1,0,1,0,1,1,0,0,0,1,0]
 => [2,3,5,4,1,6] => [2,3,5,4,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,0,1,1,0,0,1,0,0,1,0]
 => [2,4,3,5,1,6] => [2,4,3,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,0,1,1,0,1,0,0,0,1,0]
 => [2,4,5,3,1,6] => [2,4,5,3,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,0,1,1,1,0,0,0,0,1,0]
 => [2,5,4,3,1,6] => [2,5,4,3,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,1,0,0,1,0,1,0,0,1,0]
 => [3,2,4,5,1,6] => [3,2,4,5,1] => ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,1,0,0,1,1,0,0,0,1,0]
 => [3,2,5,4,1,6] => [3,2,5,4,1] => ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 1
[1,1,1,0,1,0,0,1,0,0,1,0]
 => [3,4,2,5,1,6] => [3,4,2,5,1] => ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,1,0,1,0,1,0,0,0,1,0]
 => [3,4,5,2,1,6] => [3,4,5,2,1] => ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,1,0,1,1,0,0,0,0,1,0]
 => [3,5,4,2,1,6] => [3,5,4,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,1,1,0,0,0,1,0,0,1,0]
 => [4,3,2,5,1,6] => [4,3,2,5,1] => ([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,1,1,0,0,1,0,0,0,1,0]
 => [4,3,5,2,1,6] => [4,3,5,2,1] => ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,1,1,0,1,0,0,0,0,1,0]
 => [4,5,3,2,1,6] => [4,5,3,2,1] => ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,1,1,1,0,0,0,0,0,1,0]
 => [5,4,3,2,1,6] => [5,4,3,2,1] => ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 1
[1,1,0,1,0,1,0,1,0,1,0,0,1,0]
 => [2,3,4,5,6,1,7] => [2,3,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)
 => 1
[1,1,0,1,0,1,0,1,1,0,0,0,1,0]
 => [2,3,4,6,5,1,7] => [2,3,4,6,5,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,0,1,0,1,1,0,0,1,0,0,1,0]
 => [2,3,5,4,6,1,7] => [2,3,5,4,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,0,1,0,1,1,0,1,0,0,0,1,0]
 => [2,3,5,6,4,1,7] => [2,3,5,6,4,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,0,1,0,1,1,1,0,0,0,0,1,0]
 => [2,3,6,5,4,1,7] => [2,3,6,5,4,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,0,1,1,0,0,1,0,1,0,0,1,0]
 => [2,4,3,5,6,1,7] => [2,4,3,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,0,1,1,0,0,1,1,0,0,0,1,0]
 => [2,4,3,6,5,1,7] => [2,4,3,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 1
[1,1,0,1,1,0,1,0,0,1,0,0,1,0]
 => [2,4,5,3,6,1,7] => [2,4,5,3,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,0,1,1,0,1,0,1,0,0,0,1,0]
 => [2,4,5,6,3,1,7] => [2,4,5,6,3,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,0,1,1,0,1,1,0,0,0,0,1,0]
 => [2,4,6,5,3,1,7] => [2,4,6,5,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,0,1,1,1,0,0,0,1,0,0,1,0]
 => [2,5,4,3,6,1,7] => [2,5,4,3,6,1] => ([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,0,1,1,1,0,0,1,0,0,0,1,0]
 => [2,5,4,6,3,1,7] => [2,5,4,6,3,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,0,1,1,1,0,1,0,0,0,0,1,0]
 => [2,5,6,4,3,1,7] => [2,5,6,4,3,1] => ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,0,1,1,1,1,0,0,0,0,0,1,0]
 => [2,6,5,4,3,1,7] => [2,6,5,4,3,1] => ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,1,0,0,1,0,1,0,1,0,0,1,0]
 => [3,2,4,5,6,1,7] => [3,2,4,5,6,1] => ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,1,0,0,1,0,1,1,0,0,0,1,0]
 => [3,2,4,6,5,1,7] => [3,2,4,6,5,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 1
[1,1,1,0,0,1,1,0,0,1,0,0,1,0]
 => [3,2,5,4,6,1,7] => [3,2,5,4,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 1
[1,1,1,0,0,1,1,0,1,0,0,0,1,0]
 => [3,2,5,6,4,1,7] => [3,2,5,6,4,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,1,0,0,1,1,1,0,0,0,0,1,0]
 => [3,2,6,5,4,1,7] => [3,2,6,5,4,1] => ([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,1,0,1,0,0,1,0,1,0,0,1,0]
 => [3,4,2,5,6,1,7] => [3,4,2,5,6,1] => ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,1,0,1,0,0,1,1,0,0,0,1,0]
 => [3,4,2,6,5,1,7] => [3,4,2,6,5,1] => ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,1,0,1,0,1,0,0,1,0,0,1,0]
 => [3,4,5,2,6,1,7] => [3,4,5,2,6,1] => ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,1,0,1,0,1,0,1,0,0,0,1,0]
 => [3,4,5,6,2,1,7] => [3,4,5,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,1,0,1,0,1,1,0,0,0,0,1,0]
 => [3,4,6,5,2,1,7] => [3,4,6,5,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,1,0,1,1,0,0,0,1,0,0,1,0]
 => [3,5,4,2,6,1,7] => [3,5,4,2,6,1] => ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,1,0,1,1,0,0,1,0,0,0,1,0]
 => [3,5,4,6,2,1,7] => [3,5,4,6,2,1] => ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
[1,1,1,0,1,1,0,1,0,0,0,0,1,0]
 => [3,5,6,4,2,1,7] => [3,5,6,4,2,1] => ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 1
Description
The radius of a connected graph. This is the minimum eccentricity of any vertex.