

A112918


Number of nonisomorphic connected Hgraphs H(n:i,j;k,m) on 6n vertices (or nodes) for 1<=i,j,k,m<n/2.


2



1, 1, 4, 5, 7, 12, 18, 27, 24, 69, 41, 70, 111, 103, 87, 202, 115, 275, 268, 284, 201, 583, 313, 482, 459, 708, 403, 1347
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OFFSET

3,3


COMMENTS

An Hgraph 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,...,n1 and subscript addition is performed modulo n. Hgraph H(n:i,j;k,m) is connected if and only if gcd(n,i,j,k,m) = 1.


REFERENCES

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


LINKS



EXAMPLE

The only connected symmetric Hgraphs are H(17:1,4;2,8) and H(34:1,13;9,15) which are also listed in Foster's Census.


CROSSREFS



KEYWORD

nonn,more


AUTHOR

Marko Boben (Marko.Boben(AT)fmf.unilj.si), Tomaz Pisanski and Arjana Zitnik (Arjana.Zitnik(AT)fmf.unilj.si), Oct 06 2005


STATUS

approved



