A081809 Number n-cyclic graphs.

1, 3, 3, 10, 12, 35, 58, 160, 341, 958, 2444, 7242, 21190, 67217, 217335

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

Table of n, a(n) for n=3..17.

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

Sequence in context: A332955 A355089 A218953 * A359894 A236170 A129885

Adjacent sequences: A081806 A081807 A081808 * A081810 A081811 A081812

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

Status

approved