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Counting 2-circulant graphs

Part of: Graph theory

Published online by Cambridge University Press:  09 April 2009

Gek-Ling Chia  and
Chong-Keang Lim
Gek-Ling Chia
Affiliation:
Department of MathematicsUniversity of MalayaKuala Lumpur 22-11, Malaysia
Chong-Keang Lim
Affiliation:
Department of MathematicsUniversity of MalayaKuala Lumpur 22-11, Malaysia
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Abstract

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Alspach and Sutcliffe call a graph X(S, q, F) 2-circulant if it consists of two isomorphic copies of circulant graphs X(p, S) and X(p, qS) on p vertices with “cross-edges” joining one another in a prescribed manner. In this paper, we enumerate the nonisomorphic classes of 2-circulant graphs X(S, q, F) such that |S| = m and |F| = k. We also determine a necessary and sufficient condition for a 2-circulant graph to be a GRR. The nonisomorphic classes of GRR on 2p vertices are also enumerated.

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 05C30: Enumeration in graph theory 05C99: None of the above, but in this section

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 39 , Issue 2 , October 1985 , pp. 270 - 281
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Alspach, B., ‘Point-symmetric graphs and digraphs of prime order and transitive permutation groups of prime degree’, J. Combin. Theory Ser. B. 15 (1973), 12–17.CrossRefGoogle Scholar
[2]Alspach, B. and Sutcliffe, R., ‘Vertex-transitive graphs of order 2p,’ Ann. New York Acad. Sci. 319 (1979), 18–27.CrossRefGoogle Scholar
[3]Babai, L., ‘Isomorphism problem for a class of point symmetric structures’, Acta Math. Acad. Sci. Hungar. 29 (1977), 329–336.CrossRefGoogle Scholar
[4]Chia, G. L. and Lim, C. K., ‘A class of self-complementary vertex-transitive digraphs,’ J. Combin. Theory, to appear.Google Scholar
[5]Chia, G. L., A class of strongly vertex transitive digraphs, (M. Sc. Thesis, University of Malaya, 1979).Google Scholar
[6]Doyle, J. K., ‘Weak starred polygons and Cayley graphs,’ Nanta Math. 11 (1978), 7–9.Google Scholar
[7]Elspas, B. and Turner, J., ‘Graphs with circulant adjecency matrices,’ J. Combin. Theory 9 (1970), 297–307.CrossRefGoogle Scholar
[8]Godsil, C. D., ‘On Cayley graph isomorphisms,’ Research Report No. 21, 1977, University of Melbourne.Google Scholar
[9]Godsil, C. D., ‘Unsolved Problems,’ Summer Research Workshop in Algebraic Combinatorics, 07 1979, Simon Fraser University.Google Scholar
[10]Harary, F., Graph theory (Addison-Wesley, Reading, Menlo Park, London, 1969).CrossRefGoogle Scholar
[11]Sabidussi, G., ‘On a class of fixed-point-free graphs,’ Proc. Amer. Math. Soc. 9 (1958), 800–804.CrossRefGoogle Scholar
[12]Turner, J., ‘Point-symmetric graphs with a prime number of points,’ J. Combin. Theory 3 (1967), 136–145.CrossRefGoogle Scholar
[13]Watkins, M. E., ‘On the action of non-Abelian groups on graphs,’ J. Combin. Theory 11 (1971), 95–104.CrossRefGoogle Scholar