Journal of Prime Research in Mathematics

# g-noncommuting graph of some finite groups

M. Nasiri
A. Erfanian
Department of Pure Mathematics and Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad, Mashhad, Iran.
M. Ganjali
$$^{1}$$Corresponding Author: mahnasiri@yahoo.com
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 $$[x, y] \neq g$$ 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.