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}