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A112920
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.
4
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
OFFSET
3,5
COMMENTS
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.
REFERENCES
I. Z. Bouwer, W. W. Chernoff, B. Monson, and Z. Starr (Editors), "Foster's Census", Charles Babbage Research Centre, Winnipeg, 1988.
LINKS
J. D. Horton and I. Z. Bouwer, Symmetric Y-graphs and H-graphs, J. Comb. Theory B 53 (1991) 114-129.
EXAMPLE
The smallest H-graph with girth 6 is H(6:1,1;1,1).
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), Tomaz Pisanski and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), Oct 06 2005
STATUS
approved