Prime labeling of certain graphs

Abstract

A graph $G=\left(V,E\right)$ 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 label of each pair of adjacent vertices are relatively prime. In this paper we obtain the prime labeling for the middle graph of path, kite graph, one point union of shell graphs and the subdivided shell graph with star graph.