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

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.