Algebra

Volume 2013 (2013), Article ID 107265, 7 pages

http://dx.doi.org/10.1155/2013/107265

## The Cyclic Graph of a Finite Group

^{1}School of Mathematical Sciences, Guangxi Teachers Education University, Nanning 530023, China^{2}College of Mathematics and Information Science, Guangxi University, Nanning 530004, China

Received 17 January 2013; Accepted 11 March 2013

Academic Editor: Mohammad Reza Darafsheh

Copyright © 2013 Xuan Long Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The cyclic graph of a finite group is as follows: take as the vertices of and join two distinct vertices and if is cyclic. In this paper, we investigate how the graph theoretical properties of affect the group theoretical properties of . First, we consider some properties of and characterize certain finite groups whose cyclic graphs have some properties. Then, we present some properties of the cyclic graphs of the dihedral groups and the generalized quaternion groups for some . Finally, we present some parameters about the cyclic graphs of finite noncyclic groups of order up to .