the non-commuting graph $nabla(g)$ of a non-abelian group $g$ is defined as follows: its vertex set is $g-z(g)$ and two distinct vertices $x$ and $y$ are joined by an edge if and only if the commutator of $x$ and $y$ is not the identity. in this paper we 'll prove that if $g$ is a finite group with $nabla(g)congnabla(bs_{n})$, then $g cong bs_{n}$, where $bs_{n}$ is the symmetric group of degre...

For a nite group G the commutativity degree denote by d(G) and dend:$$d(G) =frac{|{(x; y)|x, yin G,xy = yx}|}{|G|^2}.$$ In [2] authors found commutativity degree for some groups,in this paper we nd commutativity degree for a class of groups that have high nilpontencies.