The L(2, 1)-labeling of K1, n-free graphs and its applications

An L(2, 1)-labeling of a graph G is a function f from the vertex set V (G) into the set of nonnegative integers such that | f (x) − f (y)| ≥ 2 if d(x, y) = 1 and | f (x) − f (y)| ≥ 1 if d(x, y) = 2, where d(x, y) denotes the distance between x and y in G. The L(2, 1)-labeling number, λ(G), of G is the minimum k where G has an L(2, 1)-labeling f with k being the absolute difference between the largest and smallest image points of f . In this work, we will study the L(2, 1)-labeling on K1,n-free graphs where n ≥ 3 and apply the result to unit sphere graphs which are of particular interest in the channel assignment problem. c © 2008 Elsevier Ltd. All rights reserved.