TY - JOUR T1 - OD-characterization of Almost Simple Groups Related to displaystyle D4(4) TT - JF - IJMSI JO - IJMSI VL - 10 IS - 1 UR - http://ijmsi.ir/article-1-382-en.html Y1 - 2015 SP - 23 EP - 43 KW - Degree pattern KW - $k$-fold OD-characterizable KW - Almost simple group. N2 - Let $G$ be a finite group and $pi_{e}(G)$ be the set of orders of all elements in $G$. The set $pi_{e}(G)$ determines the prime graph (or Grunberg-Kegel graph) $Gamma(G)$ whose vertex set is $pi(G)$, the set of primes dividing the order of $G$, and two vertices $p$ and $q$ are adjacent if and only if $pqinpi_{e}(G)$. The degree $deg(p)$ of a vertex $pin pi(G)$, is the number of edges incident on $p$. Let $pi(G)={p_{1},p_{2},...,p_{k}}$ with $p_{1} M3 10.7508/ijmsi.2015.01.003 ER -