European Journal of Molecular & Clinical Medicine2515-82607720201224Prime Distance Labeling Of The Non-Commuting Graph Of Some Non-Abelian Groups391939265240ENA. ParthibanDepartment of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Phagwara-144 411, Punjab, IndiaRam DayalDepartment of Mathematics, School of Chemical Engineering and Physical Sciences, Lovely Professional University, Phagwara-144 411, Punjab, IndiaSwati SharmaPathways School Gurgaon, Gurugram- 122 003, Haryana, IndiaJournal Article20201224A 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.https://ejmcm.com/article_5240_317bc9cc80c663932e2a83295ef54cd0.pdf