European Journal of Molecular & Clinical Medicine

A graph 𝑮(𝑽,𝑬) is said to admit a prime distance labeling if there exists an one-to-one function 𝒉∶ 𝑽 (𝑮)→𝒁 such that |𝒉(𝒖)− 𝒉(𝒗)| is a prime number for every pair of adjacent vertices 𝒖 and 𝒗 in 𝑮. In this paper, we investigate if the prime distance labeling of the non-commuting graph of non-abelian groups such as symmetric group (𝑺𝒏,𝒐), dihedral group 𝑫𝟐𝒏,𝒏∈𝑵 exists or not.