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Search: id:A107456
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| A107456 |
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Number of nonisomorphic generalized Petersen graphs P(n,k) with girth 7 on n vertices for 1<=k<=Floor[(n-1)/2]. |
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| 1, 1, 1, 1, 2, 1, 2, 1, 3, 2, 2, 0, 2, 2, 2, 4, 2, 1, 2, 2, 2, 2, 5, 1, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 1, 5, 2, 2, 2, 2, 1, 2, 5, 2, 2, 2, 1, 2, 2, 5, 2, 2, 1, 2, 2, 2, 5, 2, 1, 2, 2, 2, 2, 5, 1, 2, 2, 2, 2, 2, 4, 2, 2, 2, 2, 2, 1, 5, 2, 2, 2, 2, 1, 2, 5, 2, 2
(list; graph; listen)
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OFFSET
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13,5
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COMMENT
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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
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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
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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
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A generalized Petersen graph P(n,k) has girth 7 if and only if it has girth more than 6 and (n=7k or 2n=7*k or 3n=7k or k=4 or 4k=n+1 or 4=n-k or 4k=n-1 or 4k=2n-1 or 3k=n+2 or 3=n-2k or 3k=n-2)
The smallest generalized Petersen graph with girth 7 is P(13,5)
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CROSSREFS
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Cf. A077105, A107452-A107460.
Sequence in context: A134583 A087467 A128118 this_sequence A165112 A077480 A059829
Adjacent sequences: A107453 A107454 A107455 this_sequence A107457 A107458 A107459
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KEYWORD
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nonn
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AUTHOR
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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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