Abstract: A graph ????(????, ????) is said to admit a prime distance labeling if there exists an oneto-one function ???? ∶ ???? (????) → ???? such that |????(????) − ????(????)| is a prime number for every pair of adjacent vertices ???? and ???? in ????. In this paper, we investigate if the prime distance labeling of the non-commuting graph of non-abelian groups such as symmetric group (????????, ????), dihedral group ????????????, ???? ∈ ???? exists or not.