Permutability graph of cyclic subgroups of some finite groups

R. Rajkumara,* and P. Devib

Permutability graph of cyclic subgroups of some finite groups

Authors :

R. Rajkumar^a,* and P. Devi^b

Author Address :

^a,bDepartment of Mathematics, The Gandhigram Rural Institute-Deemed University, Gandhigram-624 302, Tamil Nadu, India.

*Corresponding author.

Abstract :

Let $G$ be a group. \textit{The permutability graph of cyclic subgroups of $G$}, denoted by $\Gamma_c(G)$, is a graph with all the proper cyclic subgroups of $G$ as its vertices and two distinct vertices in $\Gamma_c(G)$ are adjacent if and only if the corresponding subgroups permute in $G$. In this paper, we give the structure and properties of $\Gamma_c(G)$, when $G$ is one of dihedral group, quaternion group or quasi-dihedral group.

Keywords :

Permutability graph, cyclic subgroup, non-abelian groups.

DOI :

Article Info :

Received : May 22, 2015; Accepted : June 09, 2015.