Commuting Graphs, <i>C</i>(<i>G</i>, <i>X</i>) in Symmetric Groups Sym(<i>n</i>) and Its Connectivity

Abstract

A commuting graph is a graph denoted by C ( G , X ) where G is any group and X, a subset of a group G, is a set of vertices for C ( G , X ) . Two distinct vertices, x , y ∈ X , will be connected by an edge if the commutativity property is satisfied or x y = y x . This study presents results for the connectivity of C ( G , X ) when G is a symmetric group of degree n, Sym ( n ) , and X is a conjugacy class of elements of order three in G.

Keywords

• commuting graph
• symmetric group
• order 3 elements