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A363363
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.
2
0, 0, 0, 0, 0, 4, 26, 209, 1513, 12145
OFFSET
1,6
LINKS
Stephan Brandt, Ralph Faudree, and Wayne Goddard, Weakly pancyclic graphs, Journal of Graph Theory 27 (1998), 141-176.
FORMULA
a(n) = A001349(n) - A363362(n).
a(n) = 0 for n <= 5, because all graphs on at most 5 nodes are weakly pancyclic.
EXAMPLE
There are a(6) = 4 not weakly pancyclic graphs on 6 nodes (all of them connected):
a cycle of length 6 with one additional edge (two different graphs);
the complete bipartite graph K_{3,3} with one edge removed;
K_{3,3}.
CROSSREFS
KEYWORD
nonn,more
AUTHOR
STATUS
approved