Radio Number for Generalized Petersen Graphs P(n,2)

Abstract

Let G be a connected graph and d(μ,ω) be the distance between any two vertices of G. The diameter of G is denoted by diam(G) and is equal to max{d(μ,ω); μ, ω ∈ G}. The radio labeling (RL) for the graph G is an injective function F : V(G) → N ∪ {0} such that for any pair of vertices μ and ω |F(μ) - F(ω)|≥ diam(G)-d(μ,ω)+1. The span of radio labeling is the largest number in F(V). The radio number of G, denoted by rn(G) is the minimum span over all radio labeling of G. In this paper, we determine radio number for the generalized Petersen graphs, P(n,2), n=4k+2. Further the lower bound of radio number for P(n,2) when n=4k is determined.