اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدProof of a conjecture of Abdollahi-Akbari-Maimani concerning the non-commutative graph of finite groups
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The non--commuting graph $Gamma(G)$ of a non--abelian group $G$ is defined as follows. The vertex set $V(Gamma(G))$ of $Gamma(G)$ is $Gsetminus Z(G)$ where $Z(G)$ denotes the center of $G$ and two vertices $x$ and $y$ are adjacent if and only if $xy eq yx$. For non--abelian finite groups $G$ and $H$ it is conjectured that if $Gamma(G) cong Gamma(H)$, then $|G|=|H|$. We prove the conjecture.
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