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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
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

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