### PRIME LABELING IN THE CONTEXT OF DUPLICATION OF VERTICES

#### Abstract

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 _{ , }wheel ,Gear graph ,Friendship graph and Double triangular snake . We discuss prime labeling in the context of the graph operation namely duplication.

*Keywords***: **Graph Labeling, Prime Labeling, Duplication, Prime Graphs.

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