Radio Number for Special Family of Graphs with Diameter 2,3 and 4

Abstract

A radio labeling of a graph G is an injective function f : V(G) ®NÈ {0} such that for every u, v ÎV(G), ³ diam (G) – d(u, v)+1. The span of f is the difference of the largest and the smallest channels used, that is,max {f(u) - f(v)} where u,v are any two vertices of G.

The radio number of G is defined as the minimum span of a radio labeling of G and denoted as rn(G).  In this paper, we present algorithms to get the radio labeling of special family of graphs like double cones, books and nC₄ with a common vertex whose diameters are 2,3 and 4 respectively.