\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
\quad\,In a manner analogous to the commutative case, the
zero-divisor graph of a non-commutative ring $R$ can be defined as
the directed graph $\mathnormal{\Gamma}(R)$ that its vertices are
all non-zero zero-divisors of $R$ in which for any two distinct
vertices $x$ and $y$, $x\rightarrow y$ is an edge if and only if
$xy=0$. We investigate the interplay between the ring-theoretic
properties of $R$ and the graph-theoretic properties of
$\mathnormal{\Gamma}(R)$. In this paper it is shown that, with
finitely many exceptions, if $R$ is a ring and $S$ is a finite
semisimple ring which is not a field and
$\mathnormal{\Gamma}(R)\simeq \mathnormal{\Gamma} (S)$, then
$R\simeq S$. For any finite field $F$ and each integer $n\geqslant
2$, we prove that if $R$ is a ring and $\mathnormal{\Gamma}(R)\simeq
\mathnormal{\Gamma}(M_n(F))$, then $R\simeq M_n(F)$. Redmond defined
the simple undirected graph $\overline{\mathnormal{\Gamma}}(R)$
obtaining by deleting all directions on the edges in
$\mathnormal{\Gamma}(R)$. We classify all ring $R$ whose
$\overline{\mathnormal{\Gamma}}(R)$ is a complete graph, a bipartite
graph or a tree.}
\end{document}