On π -Product Involution Graphs in Symmetric Groups

Abstract

Suppose that G is a group, X a subset of G and π a set of natural numbers. The π-product graph Pπ(G, X) has X as its vertex set and distinct vertices are joined by an edge if the order of their product is in π. If X is a set of involutions, then Pπ(G, X) is called a π-product involution graph. In this paper we study the connectivity and diameters of Pπ(G, X) when G is a finite symmetric group and X is a G-conjugacy class of involutions.