#### Document Type

Journal Article

#### Department/Unit

Department of Mathematics

#### Title

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

#### Language

English

#### Abstract

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. © 2008 Elsevier Ltd. All rights reserved.

#### Keywords

Channel assignment, K1, n-free simple graph, L (2, 1)-labeling, Unit sphere graph

#### Publication Date

2008

#### Source Publication Title

Applied Mathematics Letters

#### Volume

21

#### Issue

11

#### Start Page

1188

#### End Page

1193

#### Publisher

Elsevier

#### ISSN (print)

08939659

#### Recommended Citation

Shao, Zhendong,
Roger K. Yeh,
Kin Keung Poon,
and
Wai Chee Shiu.
"The L(2,1)-labeling of K1,n-free graphs and its applications."
*Applied Mathematics Letters*
21.11
(2008): 1188-1193.