A363362 Number of connected weakly pancyclic graphs on n unlabeled nodes.

1, 1, 2, 6, 21, 108, 827, 10908, 259567, 11704426

Offset: 1

Author

Pontus von Brömssen, May 29 2023

Keywords

• nonn
• more

Comments

A graph is weakly pancyclic if it contains cycles of all lengths between its girth and its circumference. Acyclic graphs are considered to be weakly pancyclic. The concept of weak pancyclicity was introduced by Brandt, Faudree, and Goddard (1998).

Links

• Stephan Brandt, Ralph Faudree, and Wayne Goddard, Weakly pancyclic graphs, Journal of Graph Theory 27 (1998), 141-176.

Crossrefs

Cf. A001349, A286684, A363363, A363364.

Formula

a(n) = A001349(n) - A363363(n).

a(n) = A001349(n) for n <= 5, because all graphs on at most 5 nodes are weakly pancyclic.