A382181 Number of unlabeled graphs with n vertices (including disconnected graphs) which are squares.

1, 1, 2, 3, 6, 11, 28, 77, 307, 1688, 14620, 197050, 4137271

Offset: 0

Author

Brendan McKay and Sean A. Irvine, Mar 17 2025

Keywords

• nonn
• more

Comments

If G is an unlabeled finite simple graph, define its square S(G) to be the graph with the same vertices as G. The edges of S(G) are the edges of G together with an edge from vertex u to v whenever u and v are not adjacent in G but are joined by a path of length 2.

References

• Frank Harary and Ian C. Ross, The Square of a Tree, Bell Labs Memorandum MM-59-122-2, May 16, 1959, 11 pages.

Links

• A. Mukhopadhyay, The Square Root of a Graph, J Comb. Th., 2, (1967), 290-295.
• Ian C. Ross and Frank Harary, The square of a tree, The Bell System Technical J, 39, 3, May 1960.

Crossrefs

Euler transform of A382180.