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.

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

Offset

3,6

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

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

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

Example

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

Crossrefs

Cf. A112917, A112918, A112920.

Sequence in context: A362209 A343722 A035622 * A019201 A137660 A123583

Adjacent sequences: A112916 A112917 A112918 * A112920 A112921 A112922

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