Worrawate Leela-Apiradee and Yotsanan Meemark

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 18, 2012, Number 3, Pages 20—34

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## Details

### 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

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

## Related papers

## Cite this paper

APA Leela-Apiradee, W., & Meemark Y. (2012). Isomorphism testings for graph *C _{G}*(

*a*,

*b*), Notes on Number Theory and Discrete Mathematics, 18(3), 20-34.

Leela-Apiradee, W., and Yotsanan Meemark. “Isomorphism Testings for Graph *C _{G}*(

*a*,

*b*).” Notes on Number Theory and Discrete Mathematics 18, no. 3 (2012): 20-34.

Leela-Apiradee, W., and Yotsanan Meemark. “Isomorphism Testings for Graph *C _{G}*(

*a*,

*b*).” Notes on Number Theory and Discrete Mathematics 18.3 (2012): 20-34. Print.