Isomorphism testings for graph C_G(a, b)

Worrawate Leela-Apiradee and Yotsanan Meemark
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 18, 2012, Number 3, Pages 20–34
Full paper (PDF, 234Kb

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Authors and affiliations

Worrawate Leela-Apiradee
Department of Mathematics and Computer Science
Faculty of Science, Chulalongkorn University
Bangkok, 10330 Thailand

Yotsanan Meemark
Department of Mathematics and Computer Science
Faculty of Science, Chulalongkorn University
Bangkok, 10330 Thailand

Abstract

Let G be a finite abelian group such that G ≠ {0} and a, b ∈ G \ {0}. Let C_G(a, b) be the graph whose vertex set is G and the edge set is given by
E = {{x, x + a}, {x, x + b}, {x, x − a}, {x, x − b} : x ∈ G}.
In this work, we use the properties of finite abelian group to derive isomorphism testing on the graph C_G(a, b) defined above. We study classes of isomorphic graphs. This work generalizes Nicoloso and Pietropaoli’s paper [2].

Keywords

• Circulant graph
• Finite abelian group
• Isomorphism classes

AMS Classification

• 05C25

References

1. Fraleigh, J. B. A First Course in Abstract Algebra, 7th edn, Pearson Education, Kingston, 2003.
2. Nicoloso, S., U. Pietropaoli, Isomorphism testing for circulant graphs, Tech. Rep, Vol. 664, 2007, IASI-CNR, Rome, Italy.