en تخصصي Special پژوهشي Research paper 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} Degree pattern, $k$-fold OD-characterizable, Almost simple group. 23 43 http://ijmsi.ir/browse.php?a_code=A-10-415-1&slc_lang=en&sid=1 G. R. Rezaeezadeh rezaeezadeh@sci.sku.ac.ir 10031947532846006248 10031947532846006248 Yes university of shahrekord M. R. Darafsheh darafsheh@ut.ac.ir 10031947532846006249 10031947532846006249 No university of tehran M. Bibak m.bibak62@gmail.com 10031947532846006250 10031947532846006250 No university of shahrekord M. Sajadi sajadi−mas@yahoo.com 10031947532846006251 10031947532846006251 No university of shahrekord