كليدواژه :
Non , commuting graph , almost simple group , prime graph , OD , characterization , isomorphism
چكيده فارسي :
Let $G$ be a non-abelian finite group and $Z(G)$ be the center of
$G$. The non-commuting graph, $\nabla(G)$ associated to $G$ is the
graph whose vertex set is $G-Z(G)$ and two distinct vertices $x, y$
are adjacent if and only if $xy\neq yx$. We conjecture that if $G$
is an almost simple group and $H$ is a non-abelian finite group such
that $\nabla(G)\cong \nabla(H)$, then $|G|=|H|$. Among other
results, we prove that if $(G:S)$ is an almost simple group such
that $S$ is one of the Sporadic simple groups or $S$ is one of the
mentioned Lie Groups $L_2(7), L_2(8), L_2(17), L_3(3), U_3(3),
U_4(2), F_4(2), O^+_{10}(2)$ and $O^-_{10}(2)$ and $H$ is a
non-abelian group with isomorphic non-commuting graphs, then $G\cong
H$
