OD-Characterization of almost simple groups related to $L_{3}(25)$

Let $G$ be a finite group and $pi(G)$ be the set of all the prime‎ ‎divisors of $|G|$‎. ‎The prime graph of $G$ is a simple graph‎ ‎$Gamma(G)$ whose vertex set is $pi(G)$ and two distinct vertices‎ ‎$p$ and $q$ are joined by an edge if and only if $G$ has an‎ ‎element of order $pq$‎, ‎and in this case we will write $psim q$‎. ‎The degree of $p$ is the number of vertices adjacent to $p$ and is‎ ‎denoted by $deg(p)$‎. ‎If‎ ‎$|G|=p^{alpha_{1}}_{1}p^{alpha_{2}}_{2}...p^{alpha_{k}}_{k}$‎, ‎$p_{i}^{,}$s different primes‎, ‎$p_{1}