L(3,2,1)-Labeling of the Jahangir Graph

Abstract

An L(3,2,1)-labeling is a simplified model for the channel assignment problem. It is a natural generalization of the widely studied L(2,1)-labeling. An L(3,2,1)-labeling of a graph G is a function f from the vertex set V(G) to the set of positive integers such that for any two vertices x,y, if d(x,y) = 1, then │f(x) ─ f(y)│≥ 3; if d(x,y) = 2, then f(x) ─ f(y)│≥ 2; if d(x,y) = 3,then │f(x) ─ f(y)│≥ 1. The L(3,2,1)-labeling number K3(G) of G is the smallest positive integer k such that G has an L(3,2,1)-labeling with k as the maximum label. In this paper we determine the L(3,2,1)-labeling number of the Jahangir graph J4,m.