Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Notes on L(1,1) and L(2,1) labelings for n-cube

Language

English

Abstract

Suppose d is a positive integer. An L(d,1) -labeling of a simple graph G=(V,E) is a function f:V→N={0,1,2,⋯} such that |f(u)-f(v)|≥ d if dG(u,v)=1; and |f(u)-f(v)|≥ 1 if dG(u,v)=2. The span of an L(d,1) -labeling f is the absolute difference between the maximum and minimum labels. The L(d,1) -labeling number, λd(G), is the minimum of span over all L(d,1) -labelings of G. Whittlesey et al. proved that λ 2(Qn)≤ 2k+2k-q+1-2, where n≤ 2k-q and 1≤ q≤ k+1. As a consequence, λ2(Qn)≤ 2n for n≥ 3. In particular, λ 2(Q{2k-k-1)≤ 2k-1. In this paper, we provide an elementary proof of this bound. Also, we study the (1,1) -labeling number of Qn. A lower bound on λ1(Q n) are provided and λ1(Q2k-1) are determined. © 2012 Springer Science+Business Media New York.

Keywords

Channel assignment problem, Distance two labeling, n -cube

Publication Date

2014

Source Publication Title

Journal of Combinatorial Optimization

Volume

28

Issue

3

Start Page

626

End Page

638

Publisher

Springer Verlag

DOI

10.1007/s10878-012-9568-6

Link to Publisher's Edition

http://dx.doi.org/10.1007/s10878-012-9568-6

ISSN (print)

13826905

ISSN (electronic)

15732886

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