@article { author = {Rezaeezadeh, G. R. and Bibak, M. and Sajjadi, M.}, title = {Characterization of projective special linear groups in dimension three by their orders and degree patterns}, journal = {Bulletin of the Iranian Mathematical Society}, volume = {41}, number = {3}, pages = {551-580}, year = {2015}, publisher = {Iranian Mathematical Society (IMS)}, issn = {1017-060X}, eissn = {1735-8515}, doi = {}, abstract = {The prime graph $\Gamma(G)$ of a group $G$ is a graph with vertex set $\pi(G)$, the set of primes dividing the order of $G$, and two distinct vertices $p$ and $q$ are adjacent by an edge written $p\sim q$ if there is an element in $G$ of order $pq$. Let $\pi(G)=\{p_{1},p_{2},...,p_{k}\}$. For $p\in\pi(G)$, set $deg(p):=|\{q \in\pi(G)| p\sim q\}|$, which is called the degree of $p$. We also set $D(G):=(deg(p_{1}),deg(p_{2}),...,deg(p_{k}))$, where $p_{1}