Permutability graph of cyclic subgroups of some finite groups
Authors :
R. Rajkumara,* and P. Devib
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.