A107460 Number of nonisomorphic bipartite generalized Petersen graphs P(2n,k) with girth 8 on 4n vertices for 1<=k<n.

1, 0, 1, 3, 2, 1, 3, 2, 3, 3, 3, 5, 5, 3, 4, 7, 6, 4, 6, 7, 6, 9, 6, 6, 9, 6, 10, 11, 8, 7, 11, 11, 9, 13, 9, 11, 14, 9, 10, 15, 12, 12

Offset

9,4

Comments

The generalized Petersen graph P(n,k) is a graph with vertex set V(P(n,k)) = {u_0,u_1,...,u_{n-1},v_0,v_1,...,v_{n-1}} and edge set E(P(n,k)) = {u_i u_{i+1}, u_i v_i, v_i v_{i+k} : i=0,...,n-1}, where the subscripts are to be read modulo n.

References

I. Z. Bouwer, W. W. Chernoff, B. Monson and Z. Star, The Foster Census (Charles Babbage Research Centre, 1988), ISBN 0-919611-19-2.

Links

Table of n, a(n) for n=9..50.

Marko Boben, Tomaz Pisanski, Arjana Zitnik, I-graphs and the corresponding configurations, Preprint series (University of Ljubljana, IMFM), Vol. 42 (2004), 939 (ISSN 1318-4865).

M. Watkins, A theorem on Tait colorings with an application to the generalized Petersen graphs, J. Combin. Theory 6 (1969), 152-164.

Example

A generalized Petersen graph P(n,k) is bipartite if and only if n is even and k is odd; it has girth 8 if and only if it has girth more than 6
The smallest bipartite generalized Petersen graph with girth 8 is P(18,5)

Crossrefs

Cf. A077105, A107452-A107459.

Sequence in context: A229216 A087818 A112746 * A353298 A152975 A327439

Adjacent sequences: A107457 A107458 A107459 * A107461 A107462 A107463

Keyword

nonn

Author

Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), Tomaz Pisanski and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), May 26 2005

Status

approved