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A112919 Number of nonisomorphic connected bipartite H-graphs H(n:i,j;k,m) on 6n vertices (or nodes) for 1<=i,j,k,m<n/2. 3
0, 1, 0, 1, 0, 4, 0, 4, 0, 12, 0, 7, 0, 16, 0, 18, 0, 33, 0, 24, 0, 67, 0, 41, 0, 71, 0, 111 (list; graph; refs; listen; history; text; internal format)



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.


J. D. Horton and I. Z. Bouwer, Symmetric Y-graphs and H-graphs, J. Comb. Theory B 53 (1991) 114-129

I. Z. Bouwer, W. W. Chernoff, B. Monson and Z. Starr (Editors), "Foster's Census", Charles Babbage Research Centre, Winnipeg, 1988.


Table of n, a(n) for n=3..30.


The only connected symmetric bipartite H-graph is H(34:1,13;9,15) which is also listed in Foster's Census.


Cf. A112917, A112918, A112920.

Sequence in context: A241658 A256719 A035622 * A019201 A137660 A123583

Adjacent sequences:  A112916 A112917 A112918 * A112920 A112921 A112922




Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), Tomaz Pisanski and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), Oct 06 2005



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Last modified December 4 08:51 EST 2020. Contains 338921 sequences. (Running on oeis4.)