A363363 - OEIS

%I #6 Jun 02 2023 08:39:26

%S 0,0,0,0,0,4,26,209,1513,12145

%N Number of connected unlabeled n-node graphs G that are not weakly pancyclic, i.e., there exists an integer k such that G contains a cycle that is longer than k and a cycle that is shorter than k but no cycle of length k.

%H Stephan Brandt, Ralph Faudree, and Wayne Goddard, <a href="https://doi.org/10.1002/(SICI)1097-0118(199803)27:3%3C141::AID-JGT3%3E3.0.CO;2-O">Weakly pancyclic graphs</a>, Journal of Graph Theory 27 (1998), 141-176.

%F a(n) = A001349(n) - A363362(n).

%F a(n) = 0 for n <= 5, because all graphs on at most 5 nodes are weakly pancyclic.

%e There are a(6) = 4 not weakly pancyclic graphs on 6 nodes (all of them connected):

%e   a cycle of length 6 with one additional edge (two different graphs);

%e   the complete bipartite graph K_{3,3} with one edge removed;

%e   K_{3,3}.

%Y Cf. A001349, A363362, A363364.

%K nonn,more

%O 1,6

%A _Pontus von Brömssen_, May 29 2023