Values
=>
Cc0020;cc-rep
([],1)=>1
([],2)=>0
([(0,1)],2)=>1
([],3)=>-1
([(1,2)],3)=>0
([(0,2),(1,2)],3)=>1
([(0,1),(0,2),(1,2)],3)=>2
([],4)=>-2
([(2,3)],4)=>-1
([(1,3),(2,3)],4)=>0
([(0,3),(1,3),(2,3)],4)=>1
([(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)=>2
([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>3
([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>4
([],5)=>-3
([(3,4)],5)=>-2
([(2,4),(3,4)],5)=>-1
([(1,4),(2,4),(3,4)],5)=>0
([(0,4),(1,4),(2,4),(3,4)],5)=>1
([(1,4),(2,3)],5)=>-1
([(1,4),(2,3),(3,4)],5)=>0
([(0,1),(2,4),(3,4)],5)=>0
([(2,3),(2,4),(3,4)],5)=>0
([(0,4),(1,4),(2,3),(3,4)],5)=>1
([(1,4),(2,3),(2,4),(3,4)],5)=>1
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>2
([(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)=>3
([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
([(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)=>2
([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>3
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>4
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>3
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>5
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>4
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>5
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>6
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>7
([],6)=>-4
([(4,5)],6)=>-3
([(3,5),(4,5)],6)=>-2
([(2,5),(3,5),(4,5)],6)=>-1
([(1,5),(2,5),(3,5),(4,5)],6)=>0
([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>1
([(2,5),(3,4)],6)=>-2
([(2,5),(3,4),(4,5)],6)=>-1
([(1,2),(3,5),(4,5)],6)=>-1
([(3,4),(3,5),(4,5)],6)=>-1
([(1,5),(2,5),(3,4),(4,5)],6)=>0
([(0,1),(2,5),(3,5),(4,5)],6)=>0
([(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>1
([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(2,4),(2,5),(3,4),(3,5)],6)=>0
([(0,5),(1,5),(2,4),(3,4)],6)=>0
([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>1
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>1
([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>2
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>2
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>3
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>4
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,5),(1,4),(2,3)],6)=>-1
([(1,5),(2,4),(3,4),(3,5)],6)=>0
([(0,1),(2,5),(3,4),(4,5)],6)=>0
([(1,2),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>1
([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>2
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>2
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>3
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>1
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>2
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>2
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>2
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>2
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>2
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>3
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>1
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>1
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>2
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>2
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>2
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>3
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>3
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>3
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>3
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>4
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>4
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>4
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>5
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>3
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>3
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>4
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>4
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>2
([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>3
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>3
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>3
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>3
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>3
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>4
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>4
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>4
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>5
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>7
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>5
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>6
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>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)=>8
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>2
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>3
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>4
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>4
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>5
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>6
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>7
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>4
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>4
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>5
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>6
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>5
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>6
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>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)=>8
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>6
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>7
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>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)=>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)=>9
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>7
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>7
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>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)=>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)=>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)=>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)=>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)=>11
search for individual values
searching the database for the individual values of this statistic
/
search for generating function
searching the database for statistics with the same 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.
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
searching the database
Sorry, this statistic was not found in the database
or
add this statistic to the database – it's very simple and we need your support!