Some New Families of Prime Labeling of Graphs

A Graph G with n vertices is said to admit prime labeling if its vertices can be labeled with distinct positive integers not exceeding n such that the labels of each pair of adjacent vertices are relatively prime. A graph G which admits prime labeling is called a prime graph. In this paper we investigate the existence of prime labeling of some graphs related to cycle Cn, wheel W_n, comb P_n^*, crown C_n^*, and helm H_n. We discuss prime labeling in the context of the graph operation namely duplication.