Identifier
Values
=>
Cc0020;cc-rep
([],1)=>1 ([],2)=>1 ([(0,1)],2)=>2 ([],3)=>1 ([(1,2)],3)=>2 ([(0,2),(1,2)],3)=>3 ([(0,1),(0,2),(1,2)],3)=>2 ([],4)=>1 ([(2,3)],4)=>2 ([(1,3),(2,3)],4)=>3 ([(0,3),(1,3),(2,3)],4)=>4 ([(0,3),(1,2)],4)=>2 ([(0,3),(1,2),(2,3)],4)=>4 ([(1,2),(1,3),(2,3)],4)=>2 ([(0,3),(1,2),(1,3),(2,3)],4)=>3 ([(0,2),(0,3),(1,2),(1,3)],4)=>3 ([(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)=>2 ([],5)=>1 ([(3,4)],5)=>2 ([(2,4),(3,4)],5)=>3 ([(1,4),(2,4),(3,4)],5)=>4 ([(0,4),(1,4),(2,4),(3,4)],5)=>5 ([(1,4),(2,3)],5)=>2 ([(1,4),(2,3),(3,4)],5)=>4 ([(0,1),(2,4),(3,4)],5)=>3 ([(2,3),(2,4),(3,4)],5)=>2 ([(0,4),(1,4),(2,3),(3,4)],5)=>6 ([(1,4),(2,3),(2,4),(3,4)],5)=>3 ([(0,4),(1,4),(2,3),(2,4),(3,4)],5)=>4 ([(1,3),(1,4),(2,3),(2,4)],5)=>3 ([(0,4),(1,2),(1,3),(2,4),(3,4)],5)=>5 ([(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>3 ([(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>4 ([(0,4),(1,3),(1,4),(2,3),(2,4),(3,4)],5)=>4 ([(0,3),(0,4),(1,3),(1,4),(2,3),(2,4)],5)=>4 ([(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)=>5 ([(0,1),(2,3),(2,4),(3,4)],5)=>2 ([(0,3),(1,2),(1,4),(2,4),(3,4)],5)=>4 ([(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)=>4 ([(0,1),(0,4),(1,3),(2,3),(2,4),(3,4)],5)=>4 ([(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)=>4 ([(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)=>3 ([(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)=>2 ([],6)=>1 ([(4,5)],6)=>2 ([(3,5),(4,5)],6)=>3 ([(2,5),(3,5),(4,5)],6)=>4 ([(1,5),(2,5),(3,5),(4,5)],6)=>5 ([(0,5),(1,5),(2,5),(3,5),(4,5)],6)=>6 ([(2,5),(3,4)],6)=>2 ([(2,5),(3,4),(4,5)],6)=>4 ([(1,2),(3,5),(4,5)],6)=>3 ([(3,4),(3,5),(4,5)],6)=>2 ([(1,5),(2,5),(3,4),(4,5)],6)=>6 ([(0,1),(2,5),(3,5),(4,5)],6)=>4 ([(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,5),(1,5),(2,5),(3,4),(4,5)],6)=>8 ([(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,5),(1,5),(2,4),(3,4)],6)=>3 ([(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>5 ([(0,5),(1,5),(2,3),(3,4),(4,5)],6)=>8 ([(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,5),(2,4),(3,4),(4,5)],6)=>7 ([(0,5),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>7 ([(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>6 ([(0,5),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>6 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>6 ([(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(0,4),(0,5),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>5 ([(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)=>2 ([(1,5),(2,4),(3,4),(3,5)],6)=>5 ([(0,1),(2,5),(3,4),(4,5)],6)=>4 ([(1,2),(3,4),(3,5),(4,5)],6)=>2 ([(0,5),(1,4),(2,3),(3,5),(4,5)],6)=>8 ([(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>4 ([(0,1),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>6 ([(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>3 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>4 ([(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>4 ([(0,5),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>6 ([(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,2),(1,4),(2,3),(3,5),(4,5)],6)=>7 ([(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>6 ([(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(0,5),(1,4),(2,3),(2,4),(3,5)],6)=>6 ([(0,1),(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,5),(1,5),(2,3),(2,4),(3,4)],6)=>3 ([(0,4),(1,2),(1,3),(2,5),(3,5),(4,5)],6)=>7 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5)],6)=>5 ([(0,4),(1,2),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(0,1),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,4),(1,4),(2,3),(2,5),(3,5),(4,5)],6)=>6 ([(0,3),(0,4),(1,2),(1,5),(2,5),(3,5),(4,5)],6)=>5 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,5),(4,5)],6)=>6 ([(0,4),(1,2),(1,5),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(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)=>6 ([(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)=>6 ([(0,3),(0,5),(1,3),(1,5),(2,4),(2,5),(3,4),(4,5)],6)=>6 ([(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(0,5),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>6 ([(0,1),(0,5),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>5 ([(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(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)=>4 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,4),(0,5),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>6 ([(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)=>5 ([(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>3 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(2,5),(3,4)],6)=>5 ([(0,3),(0,5),(1,2),(1,5),(2,4),(3,4),(4,5)],6)=>6 ([(0,5),(1,2),(1,4),(2,3),(3,4),(3,5),(4,5)],6)=>5 ([(0,1),(0,2),(1,5),(2,4),(3,4),(3,5),(4,5)],6)=>5 ([(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>5 ([(0,5),(1,3),(1,4),(2,4),(2,5),(3,4),(3,5)],6)=>7 ([(0,1),(0,5),(1,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>6 ([(0,4),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>5 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(3,5),(4,5)],6)=>5 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>6 ([(0,4),(0,5),(1,2),(1,3),(2,4),(2,5),(3,4),(3,5)],6)=>5 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(3,5),(4,5)],6)=>5 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,4),(2,5),(3,4),(3,5)],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)=>5 ([(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)=>3 ([(0,5),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(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)=>4 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>5 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5)],6)=>4 ([(0,1),(0,2),(0,3),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,5),(4,5)],6)=>4 ([(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)=>4 ([(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)=>5 ([(0,1),(0,5),(1,5),(2,3),(2,4),(3,4),(4,5)],6)=>4 ([(0,1),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(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)=>3 ([(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)=>4 ([(0,3),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,1),(0,5),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,3),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4)],6)=>5 ([(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)=>4 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,5),(4,5)],6)=>4 ([(0,3),(0,4),(0,5),(1,2),(1,4),(1,5),(2,3),(2,5),(3,4)],6)=>4 ([(0,1),(0,3),(0,5),(1,2),(1,4),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>4 ([(0,1),(0,4),(0,5),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(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)=>4 ([(0,2),(0,5),(1,3),(1,4),(1,5),(2,3),(2,4),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,4),(0,5),(1,2),(1,3),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(0,5),(1,2),(1,3),(1,4),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>4 ([(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>2 ([(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5),(4,5)],6)=>3 ([(0,4),(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),(1,3),(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)=>4 ([(0,4),(0,5),(1,2),(1,3),(1,4),(1,5),(2,3),(2,4),(2,5),(3,4),(3,5)],6)=>3 ([(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)=>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),(4,5)],6)=>3 ([(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)=>3 ([(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)=>2
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Description
The number of nonisomorphic vertex-induced subtrees.
References
[1] Mubayi, D., Verstraete, J. The number of trees in a graph arXiv:1511.07274
Code
def statistic(G):
    V = G.vertices()
    indSubG = set()
    for subV in Subsets(V):
        subG = G.subgraph(subV)
        if subG.is_tree():
            indSubG.add(subG.canonical_label().copy(immutable=True))
    return len(indSubG)
Created
Nov 24, 2015 at 17:41 by Christian Stump
Updated
Nov 25, 2015 at 11:11 by Christian Stump