on the relation between the non-commuting graph and the prime graph

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex set $g-z(g)$ where two non-central elements $x$ and $y$ are joined by an edge if and only if $xy neq yx$. let $ g $ and $ h $ be non-abelian finite groups with isomorphic non-commuting graphs. in this article, we show that if $ | z ( g ) | = | z ( h ) | $, then $ g $ and $ h $ have the same prime graphs and also, the set of orders of the maximal abelian subgroups of $ g $ and $ h $ are the same.