On the Radio Number of Simple Connected Graphs

Abstract

In this research work we are going to study a very famous and useful type of labeling called the Radio labeling, also known as multilevel distance labeling. As a mathe matical object labeling is a map between the graph components and a number set. Radio labeling of a graph is defined as g : V(G) → N, such that | g(p) − g(q) |≥ diam(G) − d(p,q) + 1 , ∀ p,q ∈ V(G). This inequality is called the radio condition. The largest number in image of V under g is called the radio condition of G. In this thesis we are going to calculate the radio labeling for cyclic joint graph CsJm. We also provide the radio number for the graph.