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.

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

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 smallest H-graph with girth 6 is H(6:1,1;1,1).

Crossrefs

Cf. A112917, A112919, A112920.

Sequence in context: A319461 A201762 A153386 * A109364 A122277 A198211

Adjacent sequences: A112917 A112918 A112919 * A112921 A112922 A112923

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