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Identifier
Values
=>
Cc0020;cc-rep
([],1)=>0 ([],2)=>0 ([(0,1)],2)=>0 ([],3)=>0 ([(1,2)],3)=>0 ([(0,2),(1,2)],3)=>0 ([(0,1),(0,2),(1,2)],3)=>0 ([],4)=>0 ([(2,3)],4)=>0 ([(1,3),(2,3)],4)=>0 ([(0,3),(1,3),(2,3)],4)=>0 ([(0,3),(1,2)],4)=>0 ([(0,3),(1,2),(2,3)],4)=>0 ([(1,2),(1,3),(2,3)],4)=>0 ([(0,3),(1,2),(1,3),(2,3)],4)=>0 ([(0,2),(0,3),(1,2),(1,3)],4)=>0 ([(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>0 ([(0,1),(0,2),(0,3),(1,2),(1,3),(2,3)],4)=>1 ([],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)=>0 ([(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)=>0 ([(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(1,3),(1,4),(2,3),(2,4)],5)=>0 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>0 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>0 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,3),(2,3),(2,4)],5)=>0 ([(0,1),(2,3),(2,4),(3,4)],5)=>0 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,4),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,4),(2,3)],5)=>0 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>0 ([(0,3),(0,4),(1,2),(1,4),(2,3),(2,4),(3,4)],5)=>0 ([(0,4),(1,2),(1,3),(2,3),(2,4),(3,4)],5)=>0 ([(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 ([(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)=>1 ([(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4)],5)=>1 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,4),(3,4)],5)=>1 ([(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 ([(0,1),(0,2),(0,3),(0,4),(1,2),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>1 ([],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)=>0 ([(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)=>0 ([(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)=>0 ([(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)=>0 ([(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)=>0 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(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)=>0 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(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)=>0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(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)=>0 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(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)=>0 ([(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)=>0 ([(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)=>0 ([(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)=>0 ([(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)=>0 ([(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)=>0 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(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)=>0 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>0 ([(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)=>0 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>0 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(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)=>0 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>0 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(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)=>0 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>0 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(1,5),(2,3),(2,4),(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)=>1 ([(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)=>1 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(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)=>1 ([(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)=>0 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>0 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>0 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>0 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(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)=>1 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(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)=>1 ([(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)=>1 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>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 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>1 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>1 ([(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)=>1 ([(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)=>0 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>0 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>0 ([(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)=>0 ([(0,4),(0,5),(1,2),(1,3),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>1 ([(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)=>0 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(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)=>1 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,3),(0,4),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>1 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(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)=>1 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(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)=>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 ([(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)=>1 ([(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)=>1 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>1 ([(0,1),(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>1 ([(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)=>1 ([(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)=>1 ([(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)=>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)=>1 ([(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)=>1
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Description
The number of triconnected components of a graph.
A connected graph is triconnected or 3-vertex connected if it cannot be disconnected by removing two or fewer vertices. An arbitrary connected graph can be decomposed as a union of biconnected (2-vertex connected) graphs, known as blocks, and each biconnected graph can be decomposed as a union of components with are either a cycle (type "S"), a cocyle (type "P"), or triconnected (type "R"). The decomposition of a biconnected graph into these components is known as the SPQR-tree of the graph.
References
[1] wikipedia:SPQR_tree
Code
def statistic(G):
    from sage.graphs.connectivity import blocks_and_cut_vertices, spqr_tree
    blocks, _ = blocks_and_cut_vertices(G)
    res = 0
    for b in blocks:
        B = G.subgraph(b)
        if len(b) > 1:
            tree = spqr_tree(B)
            for c in tree:
                if c[0] == 'R': res += 1
    return res
Created
Dec 02, 2022 at 00:55 by Harry Richman
Updated
Dec 02, 2022 at 09:23 by Harry Richman