Geodesic
A New Characterization of $PGL(2,p)$ by its Noncommuting Graph
Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 3 Cet article a éte moissonné depuis la source Bulletin of the Malaysian Mathematical Society website

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Let $G$ be a finite non-abelian group. The noncommuting graph of $G$ is denoted by $\nabla(G)$ and is defined as follows: the vertex set of $\nabla(G)$ is $G\setminus Z(G)$ and two vertices $x$ and $y$ are adjacent if and only if $xy\neq yx$. Let $p$ be a prime number. In this paper, it is proved that the almost simple group $PGL(2,p)$ is uniquely determined by its noncommuting graph. As a consequence of our results the validity of a conjecture of Thompson and another conjecture of Shi and Bi for the group $PGL(2,p)$ are proved.
Classification : 20D05, 20D60. 
@article{BMMS_2011_34_3_a21,
     author = {B. Khosravi and M. Khatami},
     title = {A {New} {Characterization} of $PGL(2,p)$ by its {Noncommuting} {Graph}},
     journal = {Bulletin of the Malaysian Mathematical Society},
     year = {2011},
     volume = {34},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/BMMS_2011_34_3_a21/}
}
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B. Khosravi; M. Khatami. A New Characterization of $PGL(2,p)$ by its Noncommuting Graph. Bulletin of the Malaysian Mathematical Society, Tome 34 (2011) no. 3. http://geodesic.mathdoc.fr/item/BMMS_2011_34_3_a21/