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A112922 Number of nonisomorphic connected Y-graphs 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,3

COMMENTS

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. 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 Y-graphs and H-graphs, J. Comb. Theory B 53 (1991) 114-129

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 edge-transitive) Y-graph 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.uni-lj.si), Tomaz Pisanski and Arjana Zitnik (Arjana.Zitnik(AT)fmf.uni-lj.si), Oct 06 2005

STATUS

approved

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Last modified April 16 18:26 EDT 2014. Contains 240626 sequences.