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A245246
Number of ways to delete an edge (up to the outcome) in the simple unlabeled graphs on n nodes.
3
0, 1, 3, 14, 74, 571, 6558, 125066, 4147388
OFFSET
1,3
COMMENTS
Also, the number of distinct pairs (G,H) of simple unlabeled graphs on n nodes, where H can be obtained from G by deletion of a single edge.
For n<6, we have a(n) = A126122(n), since the non-isomorphic edges in a graph on n<6 nodes uniquely define the result of their deletion. However, there is a graph on 6 nodes (see link below) with two non-isomorphic edges, deletion of either of which results in the same graph. Hence, for n>=6, a(n) < A126122(n).
LINKS
Max Alekseyev, Example of the graph on 6 nodes, where deletion of red or blue edge (which are non-isomorphic) results in the same graph.
Max Alekseyev et al., Removal of non-isomorphic edges results in the same graph, MathOverflow, 2014.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Max Alekseyev, Jul 15 2014
STATUS
approved