DefinePK

Abstract

Let G be a finite non-abelian group and g a fixed element of G. In 2014, Tolue et al. introduced the g-noncommuting graph of G, which was denoted by Γ^{g}_G with vertex set G and two distinct vertices x and y join by an edge if [x, y] ≠ g and g^{−1}. In this paper, we consider induced subgraph of Γ^{g}_{G} on G /Z(G) and survey some graph theoretical properties like connectivity, the chromatic and independence numbers of this graph associated to symmetric, alternating and dihedral groups.