A245246 Number of ways to delete an edge (up to the outcome) in the simple unlabeled graphs on n nodes.

0, 1, 3, 14, 74, 571, 6558, 125066, 4147388

Offset: 1

Author

Max Alekseyev, Jul 15 2014

Keywords

• nonn
• more

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

Cf. A000088, A126122