@article {
author = {Darafsheh, Mohammad Reza and Yousefzadeh, Pedram},
title = {Some results on characterization of finite group by non commuting graph},
journal = {Transactions on Combinatorics},
volume = {1},
number = {2},
pages = {41-48},
year = {2012},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2012.1180},
abstract = {The non commuting graph $\nabla(G)$ of a non-abelian finite group $G$ is defined as follows: its vertex set is $G- Z (G)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. In this paper we prove some new results about this graph. In particular we will give a new proof of Theorem 3.24 of [A. Abdollahi, S. Akbari, H. R, Maimani, Non-commuting graph of a group, J. Algebra, 298 (2006) 468-492.]. We also prove that if $G_1, G_2, \ldots, G_n$ are finite groups such that $Z(G_i)=1$ for $i=1, 2,\ldots, n$ and they are characterizable by non commuting graph, then $G_1 \times G_2 \times \cdots \times G_n$ is characterizable by non-commuting graph.},
keywords = {non commuting graph,Nilpotent groups,Finite groups},
url = {https://toc.ui.ac.ir/article_1180.html},
eprint = {https://toc.ui.ac.ir/article_1180_0ca13861eb689e095c1f50d1542a1aa7.pdf}
}