On Radio Graceful Labeling of a Graph

Abstract

For a graph , a radio labeling is a function  such that , for all . The radio number of a radio labeling f ofG is the maximum label assigned to a vertex of G. The radio number of G denoted by is taken over all radio labelingf of G. A graph G is said to be radio graceful if it has a radio labeling with . In this paper we obtain the necessary condition for a graph G with n vertices to be radio graceful and characterize the radio graceful graphs with .