A107459 - OEIS

A107459

Number of nonisomorphic bipartite generalized Petersen graphs P(2n,k) with girth 6 on 4n vertices for 1<=k<n.

1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 1, 2, 2, 2

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OFFSET

4,5

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=4..52.

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 6 if and only if it has girth more than 4 and (n=6k or k=3 or 2k=n-2 or 3k=n+1 or 3k=n-1)

The smallest bipartite generalized Petersen graph with girth 6 is P(8,3)

CROSSREFS

Cf. A077105, A107452-A107460.

Sequence in context: A003640 A359944 A359308 * A087976 A227903 A353567

Adjacent sequences: A107456 A107457 A107458 * A107460 A107461 A107462

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