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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.
3

%I #11 May 22 2024 15:15:05

%S 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,

%T 15,12,20,16,18,31,18,18,24,16,20,50,21,20,28,22,23,50,27,24,32,24,26

%N 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.

%C 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.

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

%Y Cf. A112921, A112922, A112923.

%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