OFFSET
3,2
COMMENTS
Take the graph of an n-cycle and consider all possible contractions (including no contraction at all) that do not produce self-loops. Then eliminate multiple edges and count the nonisomorphic graphs.
n-cyclic graphs are distinct simple graphs on which there exists a closed n-walk.
LINKS
Eric Weisstein's World of Mathematics, Graph Cycle
Eric Weisstein's World of Mathematics, k-Cyclic Graph
FlowProblem. C_k-graphs
EXAMPLE
a(4)=3 because the square loop gives itself and can be folded to give the tree on three vertices and the connected graph on two vertices:
._.
|_| --> |_| + \/ + |
CROSSREFS
KEYWORD
nonn,nice,more,hard
AUTHOR
Timothy K. Callahan (timcall(AT)math.la.asu.edu), Apr 10 2003
EXTENSIONS
More terms from Eric W. Weisstein, Jan 08 2014
a(18)-a(21) from Bert Dobbelaere, Jun 26 2024
STATUS
approved