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

Zhendong SHAO, Roger K. YEH, Kin Keung Eric POON, Wai Chee SHIU

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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. Copyright © 2008 Elsevier.
Original languageEnglish
Pages (from-to)1188-1193
JournalApplied Mathematics Letters
Volume21
Issue number11
DOIs
Publication statusPublished - 2008

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L(2, 1)-labeling
Labeling
Graph in graph theory
Channel Assignment Problem
Unit Sphere
Non-negative
Denote
Integer
Vertex of a graph

Citation

Shao, Z., Yeh, R. K., Poon, K. K., & Shiu, W. C. (2008). The L(2,1)-labeling of K₁,n-free graphs and its applications. Applied Mathematics Letters, 21(11), 1188-1193.

Keywords

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