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

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

Offset

1,3

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

Table of n, a(n) for n=1..10.

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

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.

Crossrefs

Cf. A001349, A286684, A363363, A363364.

Sequence in context: A079129 A305923 A130275 * A156808 A245882 A374617

Adjacent sequences: A363359 A363360 A363361 * A363363 A363364 A363365

Keyword

nonn,more

Author

Pontus von Brömssen, May 29 2023

Status

approved