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

%I A112918 #10 May 22 2024 15:14:40
%S A112918 1,1,4,5,7,12,18,27,24,69,41,70,111,103,87,202,115,275,268,284,201,
%T A112918 583,313,482,459,708,403,1347
%N A112918 Number of nonisomorphic connected H-graphs H(n:i,j;k,m) on 6n vertices (or nodes) for 1<=i,j,k,m<n/2.
%C A112918 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.
%D A112918 I. Z. Bouwer, W. W. Chernoff, B. Monson, and Z. Starr (Editors), "Foster's Census", Charles Babbage Research Centre, Winnipeg, 1988.
%H A112918 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 A112918 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.
%Y A112918 Cf. A112917, A112919, A112920.
%K A112918 nonn,more
%O A112918 3,3
%A A112918 Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), _Tomaz Pisanski_ and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), Oct 06 2005