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

Zhendong Shao*, Roger K. Yeh, Kin Keung Poon, Wai Chee SHIU

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1188-1193
Number of pages6
JournalApplied Mathematics Letters
Volume21
Issue number11
DOIs
Publication statusPublished - Nov 2008

Scopus Subject Areas

  • Applied Mathematics

User-Defined Keywords

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

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