A112924 Number of nonisomorphic connected Y-graphs Y(n:i,j,k) with girth 6 on 4n vertices (or nodes) for 1<=i,j,k<=n.

0, 0, 0, 1, 3, 2, 3, 2, 5, 3, 6, 6, 4, 4, 8, 12, 9, 4, 12, 10, 11, 19, 10, 12, 15, 12, 14, 22, 15, 12, 20, 16, 18, 31, 18, 18, 24, 16, 20, 50, 21, 20, 28, 22, 23, 50, 27, 24, 32, 24, 26

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

A Y-graph Y(n:i,j,k) has 4n vertices arranged in four segments of n vertices. Let the vertices be v_{x,y} for x=0,1,2,3 and y in the integers modulo n. The edges are v_{1,y}v_{1,y+i}, v_{2,y}v_{2,y+j}, v_{2,y}v_{2,y+k} and v_{0,y}v_{x,y}, where y=0,1,...,n-1 and x=1,2,3 and the subscript addition is performed modulo n.

Examples

			Y(6:1,1,1) is the smallest Y-graph with girth 6.
		

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. A112921, A112922, A112923.