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Search: id:A107457
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| A107457 |
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Triangle read by rows: row n gived number of nonisomorphic generalized Petersen graphs P(n,k) with girth 8 on n vertices for 1<=k<=floor[(n-1)/2]. |
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2
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| 1, 0, 0, 1, 2, 1, 4, 1, 4, 3, 2, 3, 4, 3, 5, 6, 7, 2, 7, 5, 8, 8, 8, 6, 8, 6, 10, 9, 11, 7, 13, 6, 12, 12, 13, 9, 15, 11, 13, 14, 16, 10, 17, 11, 17, 14, 17, 15, 21, 12, 19, 18, 18, 13, 23, 14, 22, 20, 22, 16, 26, 15, 24, 21, 25, 16, 26, 21, 26, 24
(list; graph; listen)
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OFFSET
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18,5
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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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Any generalized Petersen graph P(n,k) has girth at most 8; it has girth 8 if and only if it has girth more than 7.
The smallest generalized Petersen graph with girth 8 is P(18,5)
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CROSSREFS
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Cf. A077105, A107452-A107460.
Sequence in context: A072721 A035092 A160598 this_sequence A112350 A063717 A024994
Adjacent sequences: A107454 A107455 A107456 this_sequence A107458 A107459 A107460
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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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EXTENSIONS
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Example corrected by Greg Demand, Jan 17 2008
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