reviewed

approved

proposed

reviewed

editing

proposed

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

proposed

editing

editing

proposed

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

J. D. Horton and I. Z. Bouwer, <a href="https://doi.org/10.1016/0095-8956(91)90057-Q">Symmetric Y-graphs and H-graphs</a>, J. Comb. Theory B 53 (1991) 114-129.

nonn,more

approved

editing

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

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

nonn,new

nonn

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.

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

nonn,new

nonn

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.

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

3,6

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 (Eds.), "Foster's Census", Charles Babbage Research Centre, Winnipeg, 1988.

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.

nonn

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

approved