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A107459
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Number of nonisomorphic bipartite generalized Petersen graphs P(2n,k) with girth 6 on 4n vertices for 1<=k<n.
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2
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 4,5
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COMMENTS
| The generalized Petersen graph P(n,k) is a graph with vertex set $V(P(n,k)) = \{u_0,u_1,\dots,u_{n-1},v_0,v_1,\dots,v_{n-1}\}$ and edge set $E(P(n,k)) = \{u_i u_{i+1}, u_i v_i, v_i v_{i+k} : i=0,\dots,n-1\},$ where the subscripts are to be read modulo $n$.
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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.
M. Watkins, A theorem on Tait colorings with an application to the generalized Petersen graphs, J. Combin. Theory 6 (1969), 152-164.
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LINKS
| 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).
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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)
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CROSSREFS
| Cf. A077105, A107452-A107460.
Sequence in context: A095772 A175301 A003640 * A087976 A117277 A033831
Adjacent sequences: A107456 A107457 A107458 * A107460 A107461 A107462
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KEYWORD
| nonn
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AUTHOR
| Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), Tomaz Pisanski (Tomaz.Pisanski(AT)fmf.uni-lj.si) and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), May 26 2005
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