The Cyclic Graph of a Finite Group. (16th April 2013)

• Record Type: Journal Article
• Authors: Ma, Xuan Long; Wei, Hua Quan; Zhong, Guo
• Other Names: Darafsheh Mohammad Reza Academic Editor.
• Is Part Of: Algebra. Volume 2013(2013)
• Publication Date: 2013-04-16
• Subjects: Algebra -- Periodicals; Algebra; Electronic journals; Periodicals; 512.005
• DOI: 10.1155/2013/107265
• Languages: English
• ISSNs: 2314-4106

Abstract

Abstract : The cyclic graph Γ G of a finite group G is as follows: take G as the vertices of Γ G and join two distinct vertices x and y if 〈 x, y 〉 is cyclic. In this paper, we investigate how the graph theoretical properties of Γ G affect the group theoretical properties of G . First, we consider some properties of Γ G and characterize certain finite groups whose cyclic graphs have some properties. Then, we present some properties of the cyclic graphs of the dihedral groups D 2 n and the generalized quaternion groups Q 4 n for some n . Finally, we present some parameters about the cyclic graphs of finite noncyclic groups of order up to 14 .