

A112922


Number of nonisomorphic connected Ygraphs Y(n:i,j,k) on 4n vertices (or nodes) for 1<=i,j,k<n/2.


3



1, 1, 2, 3, 4, 5, 7, 8, 7, 19, 10, 16, 23, 20, 15, 33, 19, 43, 39, 37, 26, 73, 36, 52, 49, 75, 40, 127, 46, 78, 83, 87, 85, 149, 64, 109, 113, 163, 77, 227, 85, 167, 167, 158, 100, 266, 124, 222, 183, 229, 126
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OFFSET

3,3


COMMENTS

A Ygraph 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,...,n1 and x=1,2,3 and the subscript addition is performed modulo n. It is connected if and only if gcd(n,i,j,k) = 1.


REFERENCES

I. Z. Bouwer, W. W. Chernoff, B. Monson and Z. Starr (Editors), "Foster's Census", Charles Babbage Research Centre, Winnipeg, 1988.
J. D. Horton and I. Z. Bouwer, Symmetric Ygraphs and Hgraphs, J. Comb. Theory B 53 (1991) 114129


LINKS

Table of n, a(n) for n=3..53.


EXAMPLE

Y(7:1,2,3) is the Coxeter graph, the only symmetric (vertex and edgetransitive) Ygraph of girth 7 or less.


CROSSREFS

Cf. A112921, A112923, A112924.
Sequence in context: A085177 A067576 A107900 * A228683 A133017 A161924
Adjacent sequences: A112919 A112920 A112921 * A112923 A112924 A112925


KEYWORD

nonn


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



