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A112917 Number of nonisomorphic H-graphs H(n:i,j;k,m) on 6n vertices (or nodes) for 1<=i,j,k,m

%I A112917 #10 May 22 2024 15:13:13
%S A112917 1,1,4,6,7,13,19,31,24,76,41,77,116,116,87,226,115,307,276,308,201,
%T A112917 671,317,523,478,786,403,1495
%N A112917 Number of nonisomorphic H-graphs H(n:i,j;k,m) on 6n vertices (or nodes) for 1<=i,j,k,m<n/2.
%C A112917 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 A112917 I. Z. Bouwer, W. W. Chernoff, B. Monson, and Z. Starr (Editors), "Foster's Census", Charles Babbage Research Centre, Winnipeg, 1988.
%H A112917 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 A112917 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 A112917 Cf. A112918, A112919, A112920, A112921, A107452.
%K A112917 nonn,more
%O A112917 3,3
%A A112917 Marko Boben (Marko.Boben(AT)fmf.uni-lj.si), _Tomaz Pisanski_ and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), Oct 06 2005