A112918 Number of nonisomorphic connected H-graphs H(n:i,j;k,m) on 6n vertices (or nodes) for 1<=i,j,k,m

1, 1, 4, 5, 7, 12, 18, 27, 24, 69, 41, 70, 111, 103, 87, 202, 115, 275, 268, 284, 201, 583, 313, 482, 459, 708, 403, 1347

Offset: 3

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

Keywords

• nonn
• more

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. H-graph H(n:i,j;k,m) is connected if and only if gcd(n,i,j,k,m) = 1.

Examples

			The only connected symmetric H-graphs are H(17:1,4;2,8) and H(34:1,13;9,15) which are also listed in Foster's Census.
		

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.

Crossrefs

Cf. A112917, A112919, A112920.