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A112920
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Number of nonisomorphic connected bipartite H-graphs H(n:i,j;k,m) with girth 6 on 6n vertices (or nodes) for 1<=i,j,k,m<n/2.
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4
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0, 0, 0, 1, 5, 3, 5, 3, 13, 8, 19, 27, 9, 19, 33, 74, 41, 19, 61, 75, 61, 137, 51, 108, 95, 111, 99, 217
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OFFSET
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3,5
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COMMENTS
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An H-graph H(n:i,j;k,m) has 6n vertices arranged in six segments of n vertices. Let the vertices be v_{x,y} for x=0,1,2,3,4,5 and y in the integers modulo n. The edges are v_{0,y}v_{1,y}, v_{0,y}v_{2,y}, v_{0,y}v_{3,y}, v_{1,y}v_{4,y}, v_{1,y}v_{5,y} (inner edges) and v_{2,y}v_{2,y+i}, v_{3,y}v_{3,y+j}, v_{4,y}v_{3,y+k}, v_{5,y}v_{5,y+m} (outer edges) where y=0,1,...,n-1 and subscript addition is performed modulo n.
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REFERENCES
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I. Z. Bouwer, W. W. Chernoff, B. Monson and Z. Starr (Editors), "Foster's Census", Charles Babbage Research Centre, Winnipeg, 1988.
J. D. Horton and I. Z. Bouwer, Symmetric Y-graphs and H-graphs, J. Comb. Theory B 53 (1991) 114-129
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LINKS
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Table of n, a(n) for n=3..30.
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EXAMPLE
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The smallest H-graph with girth 6 is H(6:1,1;1,1).
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CROSSREFS
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Cf. A112917, A112919, A112920.
Sequence in context: A194624 A201762 A153386 * A109364 A122277 A198211
Adjacent sequences: A112917 A112918 A112919 * A112921 A112922 A112923
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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), Oct 06 2005
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STATUS
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approved
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