Identifier
Identifier
Values
([],1) generating graphics... => 1
([],2) generating graphics... => 0
([(0,1)],2) generating graphics... => 1
([],3) generating graphics... => -1
([(1,2)],3) generating graphics... => 0
([(0,2),(1,2)],3) generating graphics... => 1
([(0,1),(0,2),(1,2)],3) generating graphics... => 2
([],4) generating graphics... => -2
([(2,3)],4) generating graphics... => -1
([(1,3),(2,3)],4) generating graphics... => 0
([(1,2),(1,3),(2,3)],4) generating graphics... => 1
([(0,3),(1,3),(2,3)],4) generating graphics... => 1
([(0,3),(1,2)],4) generating graphics... => 0
([(0,3),(1,2),(2,3)],4) generating graphics... => 1
([(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 2
([(0,2),(0,3),(1,2),(1,3)],4) generating graphics... => 2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4) generating graphics... => 4
([],5) generating graphics... => -3
([(3,4)],5) generating graphics... => -2
([(2,4),(3,4)],5) generating graphics... => -1
([(2,3),(2,4),(3,4)],5) generating graphics... => 0
([(1,4),(2,4),(3,4)],5) generating graphics... => 0
([(0,4),(1,4),(2,4),(3,4)],5) generating graphics... => 1
([(1,4),(2,3)],5) generating graphics... => -1
([(1,4),(2,3),(3,4)],5) generating graphics... => 0
([(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 2
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 3
([(0,1),(2,4),(3,4)],5) generating graphics... => 0
([(0,4),(1,4),(2,3),(3,4)],5) generating graphics... => 1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 2
([(0,4),(1,3),(2,3),(2,4)],5) generating graphics... => 1
([(0,4),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 2
([(0,4),(1,2),(1,3),(2,4),(3,4)],5) generating graphics... => 2
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 4
([(0,3),(0,4),(1,2),(1,4),(2,3)],5) generating graphics... => 2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 3
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 4
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5) generating graphics... => 4
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 5
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5) generating graphics... => 5
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 6
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 7
([(0,1),(2,3),(2,4),(3,4)],5) generating graphics... => 1
([(0,3),(1,2),(1,4),(2,4),(3,4)],5) generating graphics... => 2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5) generating graphics... => 3
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5) generating graphics... => 4
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5) generating graphics... => 3
([],6) generating graphics... => -4
([(4,5)],6) generating graphics... => -3
([(3,5),(4,5)],6) generating graphics... => -2
([(3,4),(3,5),(4,5)],6) generating graphics... => -1
([(2,5),(3,5),(4,5)],6) generating graphics... => -1
([(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 1
([(2,5),(3,4)],6) generating graphics... => -2
([(2,5),(3,4),(4,5)],6) generating graphics... => -1
([(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 0
([(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 2
([(1,2),(3,5),(4,5)],6) generating graphics... => -1
([(1,5),(2,5),(3,4),(4,5)],6) generating graphics... => 0
([(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(1,5),(2,4),(3,4),(3,5)],6) generating graphics... => 0
([(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 2
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 2
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 4
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(1,2),(3,4),(3,5),(4,5)],6) generating graphics... => 0
([(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 2
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 2
([(0,1),(2,5),(3,5),(4,5)],6) generating graphics... => 0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6) generating graphics... => 1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 2
([(0,5),(1,5),(2,4),(3,4)],6) generating graphics... => 0
([(0,5),(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6) generating graphics... => 1
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,5),(1,5),(2,3),(2,4),(3,4)],6) generating graphics... => 1
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 2
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6) generating graphics... => 2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 3
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 4
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6) generating graphics... => 3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6) generating graphics... => 2
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6) generating graphics... => 3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,5),(1,4),(2,3)],6) generating graphics... => -1
([(0,1),(2,5),(3,4),(4,5)],6) generating graphics... => 0
([(0,1),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 3
([(0,1),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 2
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6) generating graphics... => 2
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 7
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 5
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 1
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6) generating graphics... => 2
([(0,5),(1,4),(2,3),(2,4),(3,5)],6) generating graphics... => 1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 3
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 2
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6) generating graphics... => 2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 3
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6) generating graphics... => 2
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 3
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 4
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 5
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 7
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 8
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 7
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 6
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6) generating graphics... => 5
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 6
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 7
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6) generating graphics... => 4
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6) generating graphics... => 3
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6) generating graphics... => 4
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 6
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 7
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6) generating graphics... => 5
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 7
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 7
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 8
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 8
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 10
([(0,1),(0,2),(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 11
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6) generating graphics... => 4
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 5
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6) generating graphics... => 5
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 6
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 7
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 8
([(0,3),(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 9
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6) generating graphics... => 7
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6) generating graphics... => 8
click to show generating function       
Description
The number of edges minus the number of vertices plus 2 of a graph.
When G is connected and planar, this is also the number of its faces.
When $G=(V,E)$ is a connected graph, this is its $k$-monochromatic index for $k>2$: for $2\leq k\leq |V|$, the $k$-monochromatic index of $G$ is the maximum number of edge colors allowed such that for each set $S$ of $k$ vertices, there exists a monochromatic tree in $G$ which contains all vertices from $S$. It is shown in [1] that for $k>2$, this is given by this statistic.
References
[1] Li, X., Wu, D. The (vertex-)monochromatic index of a graph arXiv:1603.05338
Code
def statistic(G):
    return len(G.edges())-len(G.vertices())+2
Created
Mar 29, 2016 at 11:12 by Christian Stump
Updated
Mar 30, 2016 at 09:36 by Christian Stump