Values
=>
Cc0020;cc-rep
([],1)=>0
([],2)=>0
([(0,1)],2)=>1
([],3)=>0
([(1,2)],3)=>0
([(0,2),(1,2)],3)=>1
([(0,1),(0,2),(1,2)],3)=>2
([],4)=>0
([(2,3)],4)=>0
([(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)=>0
([(0,3),(1,2),(1,3),(2,3)],4)=>1
([(0,2),(0,3),(1,2),(1,3)],4)=>2
([(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)=>3
([],5)=>0
([(3,4)],5)=>0
([(2,4),(3,4)],5)=>0
([(1,4),(2,4),(3,4)],5)=>0
([(0,4),(1,4),(2,4),(3,4)],5)=>1
([(1,4),(2,3)],5)=>0
([(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)=>0
([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>1
([(1,3),(1,4),(2,3),(2,4)],5)=>0
([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>1
([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>1
([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
([(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)=>2
([(0,4),(1,3),(2,3),(2,4)],5)=>1
([(0,1),(2,3),(2,4),(3,4)],5)=>0
([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>1
([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>1
([(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)=>2
([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>2
([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>1
([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0
([(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1
([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>2
([(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
([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3
([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4
([],6)=>0
([(4,5)],6)=>0
([(3,5),(4,5)],6)=>0
([(2,5),(3,5),(4,5)],6)=>0
([(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)=>0
([(2,5),(3,4),(4,5)],6)=>0
([(1,2),(3,5),(4,5)],6)=>0
([(3,4),(3,5),(4,5)],6)=>0
([(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)=>0
([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(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)=>0
([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>1
([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0
([(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)=>1
([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>1
([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,5),(1,4),(2,3)],6)=>0
([(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)=>0
([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1
([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1
([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>0
([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>1
([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>1
([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>1
([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>0
([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>0
([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>1
([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1
([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>1
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>1
([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>2
([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>1
([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>0
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>0
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1
([(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)=>2
([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>2
([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1
([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>1
([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,5),(1,2),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,2),(1,4),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>3
([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>3
([(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)=>3
([(0,4),(0,5),(1,2),(1,3),(2,3),(4,5)],6)=>0
([(0,2),(1,4),(1,5),(2,3),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>1
([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,1),(0,5),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,5),(3,4),(4,5)],6)=>2
([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>2
([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>2
([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>2
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>3
([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>2
([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(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)=>3
([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>2
([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2
([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0
([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1
([(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)=>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)=>3
([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>3
([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>2
([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3
([(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)=>3
([(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)=>4
([(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)=>4
([(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)=>4
([(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)=>5
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Description
The vertex connectivity of a graph.
For non-complete graphs, this is the minimum number of vertices that has to be removed to make the graph disconnected.
For non-complete graphs, this is the minimum number of vertices that has to be removed to make the graph disconnected.
References
[1] wikipedia:Vertex connectivity
[2] Triangle read by rows: T(n,k) = number of unlabeled graphs with n nodes and connectivity exactly k (n>=1, 0<=k<=n-1). OEIS:A259862
[2] Triangle read by rows: T(n,k) = number of unlabeled graphs with n nodes and connectivity exactly k (n>=1, 0<=k<=n-1). OEIS:A259862
Code
def statistic(g):
return g.vertex_connectivity()
Created
Jul 27, 2015 at 17:09 by Martin Rubey
Updated
Sep 30, 2015 at 15:35 by Martin Rubey
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