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Search: id:A112918
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| A112918 |
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Number of nonisomorphic connected H-graphs H(n:i,j;k,m) on 6n vertices (or nodes) for 1<=i,j,k,m<n/2. |
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+0
3
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| 1, 1, 4, 5, 7, 12, 18, 27, 24, 69, 41, 70, 111, 103, 87, 202, 115, 275, 268, 284, 201, 583, 313, 482, 459, 708, 403, 1347
(list; graph; listen)
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OFFSET
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3,3
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COMMENT
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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. H-graph H(n:i,j;k,m) is connected if and only if gcd(n,i,j,k,m) = 1.
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REFERENCES
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I. Z. Bouwer, W. W. Chernoff, B. Monson and Z. Starr (Eds.), "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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EXAMPLE
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The only connected symmetric H-graphs are H(17:1,4;2,8) and H(34:1,13;9,15) which are also listed in Foster's Census.
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CROSSREFS
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Cf. A112917, A112919, A112920.
Sequence in context: A079337 A160934 A032390 this_sequence A138920 A048224 A064237
Adjacent sequences: A112915 A112916 A112917 this_sequence A112919 A112920 A112921
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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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