Your data matches 2 different statistics following compositions of up to 3 maps.
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Matching statistic: St001724
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Mapping
St001724: Graphs ⟶ ℤResult quality: 100% ●values known / values provided: 100%●distinct values known / distinct values provided: 100%
Values
([],1)
 => 0
([],2)
 => 0
([(0,1)],2)
 => 0
([],3)
 => 0
([(1,2)],3)
 => 0
([(0,2),(1,2)],3)
 => 1
([(0,1),(0,2),(1,2)],3)
 => 1
([],4)
 => 0
([(2,3)],4)
 => 0
([(1,3),(2,3)],4)
 => 1
([(0,3),(1,3),(2,3)],4)
 => 2
([(0,3),(1,2)],4)
 => 0
([(0,3),(1,2),(2,3)],4)
 => 1
([(1,2),(1,3),(2,3)],4)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => 2
([],5)
 => 0
([(3,4)],5)
 => 0
([(2,4),(3,4)],5)
 => 1
([(1,4),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => 3
([(1,4),(2,3)],5)
 => 0
([(1,4),(2,3),(3,4)],5)
 => 1
([(0,1),(2,4),(3,4)],5)
 => 1
([(2,3),(2,4),(3,4)],5)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(1,3),(1,4),(2,3),(2,4)],5)
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => 3
Description
The 2-packing differential of a graph. The external neighbourhood (or boundary) of a set of vertices $S\subseteq V(G)$ is the set of vertices not in $S$ which are adjacent to a vertex in $S$. The differential of a set of vertices $S\subseteq V(G)$ is the difference of the size of the external neighbourhood of $S$ and the size of $S$. A set $S\subseteq V(G)$ is $2$-packing if the closed neighbourhoods of any two vertices in $S$ have empty intersection. The $2$-packing differential of a graph is the maximal differential of any $2$-packing set of vertices.
Matching statistic: St001723
Mapping
Mp00259: Graphs —vertex addition⟶ Graphs
St001723: Graphs ⟶ ℤResult quality: 17% ●values known / values provided: 17%●distinct values known / distinct values provided: 83%
Values
([],1)
 => ([],2)
 => 0
([],2)
 => ([],3)
 => 0
([(0,1)],2)
 => ([(1,2)],3)
 => 0
([],3)
 => ([],4)
 => 0
([(1,2)],3)
 => ([(2,3)],4)
 => 0
([(0,2),(1,2)],3)
 => ([(1,3),(2,3)],4)
 => 1
([(0,1),(0,2),(1,2)],3)
 => ([(1,2),(1,3),(2,3)],4)
 => 1
([],4)
 => ([],5)
 => 0
([(2,3)],4)
 => ([(3,4)],5)
 => 0
([(1,3),(2,3)],4)
 => ([(2,4),(3,4)],5)
 => 1
([(0,3),(1,3),(2,3)],4)
 => ([(1,4),(2,4),(3,4)],5)
 => 2
([(0,3),(1,2)],4)
 => ([(1,4),(2,3)],5)
 => 0
([(0,3),(1,2),(2,3)],4)
 => ([(1,4),(2,3),(3,4)],5)
 => 1
([(1,2),(1,3),(2,3)],4)
 => ([(2,3),(2,4),(3,4)],5)
 => 1
([(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,2),(0,3),(1,2),(1,3)],4)
 => ([(1,3),(1,4),(2,3),(2,4)],5)
 => 1
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)
 => ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => 2
([],5)
 => ([],6)
 => 0
([(3,4)],5)
 => ([(4,5)],6)
 => 0
([(2,4),(3,4)],5)
 => ([(3,5),(4,5)],6)
 => 1
([(1,4),(2,4),(3,4)],5)
 => ([(2,5),(3,5),(4,5)],6)
 => 2
([(0,4),(1,4),(2,4),(3,4)],5)
 => ([(1,5),(2,5),(3,5),(4,5)],6)
 => 3
([(1,4),(2,3)],5)
 => ([(2,5),(3,4)],6)
 => 0
([(1,4),(2,3),(3,4)],5)
 => ([(2,5),(3,4),(4,5)],6)
 => 1
([(0,1),(2,4),(3,4)],5)
 => ([(1,2),(3,5),(4,5)],6)
 => 1
([(2,3),(2,4),(3,4)],5)
 => ([(3,4),(3,5),(4,5)],6)
 => 1
([(0,4),(1,4),(2,3),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(4,5)],6)
 => 2
([(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(1,3),(1,4),(2,3),(2,4)],5)
 => ([(2,4),(2,5),(3,4),(3,5)],6)
 => 1
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)
 => 2
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,4),(1,3),(2,3),(2,4)],5)
 => ([(1,5),(2,4),(3,4),(3,5)],6)
 => 1
([(0,1),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(3,4),(3,5),(4,5)],6)
 => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)
 => ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)
 => 3
([(0,3),(0,4),(1,2),(1,4),(2,3)],5)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)
 => 1
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)
 => 2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)
 => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 2
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)
 => 3
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)
 => ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)
 => 2
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)
 => ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)
 => 3
([],7)
 => ([],8)
 => ? = 0
([(5,6)],7)
 => ([(6,7)],8)
 => ? = 0
([(4,6),(5,6)],7)
 => ([(5,7),(6,7)],8)
 => ? = 1
([(3,6),(4,6),(5,6)],7)
 => ([(4,7),(5,7),(6,7)],8)
 => ? = 2
([(2,6),(3,6),(4,6),(5,6)],7)
 => ([(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 3
([(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 4
([(0,6),(1,6),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 5
([(3,6),(4,5)],7)
 => ([(4,7),(5,6)],8)
 => ? = 0
([(3,6),(4,5),(5,6)],7)
 => ([(4,7),(5,6),(6,7)],8)
 => ? = 1
([(2,3),(4,6),(5,6)],7)
 => ([(3,4),(5,7),(6,7)],8)
 => ? = 1
([(4,5),(4,6),(5,6)],7)
 => ([(5,6),(5,7),(6,7)],8)
 => ? = 1
([(2,6),(3,6),(4,5),(5,6)],7)
 => ([(3,7),(4,7),(5,6),(6,7)],8)
 => ? = 2
([(1,2),(3,6),(4,6),(5,6)],7)
 => ([(2,3),(4,7),(5,7),(6,7)],8)
 => ? = 2
([(3,6),(4,5),(4,6),(5,6)],7)
 => ([(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(2,7),(3,7),(4,7),(5,6),(6,7)],8)
 => ? = 3
([(0,1),(2,6),(3,6),(4,6),(5,6)],7)
 => ([(1,2),(3,7),(4,7),(5,7),(6,7)],8)
 => ? = 3
([(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,7),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,6),(2,6),(3,6),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,7),(5,6),(6,7)],8)
 => ? = 4
([(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
([(0,6),(1,6),(2,6),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 5
([(3,5),(3,6),(4,5),(4,6)],7)
 => ([(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 1
([(1,6),(2,6),(3,5),(4,5)],7)
 => ([(2,7),(3,7),(4,6),(5,6)],8)
 => ? = 2
([(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 2
([(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ? = 2
([(0,6),(1,6),(2,6),(3,5),(4,5)],7)
 => ([(1,7),(2,7),(3,7),(4,6),(5,6)],8)
 => ? = 3
([(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(3,7),(4,6),(5,6),(5,7),(6,7)],8)
 => ? = 2
([(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(2,7),(3,7),(4,6),(5,6),(6,7)],8)
 => ? = 2
([(1,6),(2,6),(3,4),(3,5),(4,6),(5,6)],7)
 => ([(2,7),(3,7),(4,5),(4,6),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,6),(2,6),(3,4),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,5),(5,6),(6,7)],8)
 => ? = 3
([(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(2,7),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,6),(2,6),(3,5),(4,5),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,6),(5,6),(6,7)],8)
 => ? = 3
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 4
([(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
([(0,6),(1,6),(2,6),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,6),(5,6),(5,7),(6,7)],8)
 => ? = 4
([(0,6),(1,6),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,7),(2,7),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 5
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 2
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 2
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(5,6),(5,7)],8)
 => ? = 2
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 3
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 3
([(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,7),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,6),(2,5),(3,5),(4,5),(4,6),(5,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(5,6),(5,7),(6,7)],8)
 => ? = 3
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 4
([(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
([(0,6),(1,6),(2,5),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,7),(2,7),(3,6),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 4
([(0,6),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6),(5,6)],7)
 => ([(1,7),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7),(6,7)],8)
 => ? = 5
([(1,5),(1,6),(2,5),(2,6),(3,5),(3,6),(4,5),(4,6)],7)
 => ([(2,6),(2,7),(3,6),(3,7),(4,6),(4,7),(5,6),(5,7)],8)
 => ? = 3
Description
The differential of a graph. The external neighbourhood (or boundary) of a set of vertices $S\subseteq V(G)$ is the set of vertices not in $S$ which are adjacent to a vertex in $S$. The differential of a set of vertices $S\subseteq V(G)$ is the difference of the size of the external neighbourhood of $S$ and the size of $S$. The differential of a graph is the maximal differential of a set of vertices.