A112920 - OEIS

%I #11 May 22 2024 15:14:53

%S 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,

%T 111,99,217

%N 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.

%C 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.

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

%H 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.

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

%Y Cf. A112917, A112919, A112920.

%K nonn,more

%O 3,5

%A Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), _Tomaz Pisanski_ and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), Oct 06 2005