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
ISSN (print)
13826905
ISSN (electronic)
15732886
Recommended Citation
Zhou, Haiying, Wai Chee Shiu, and Peter Che Bor Lam. "Notes on L(1,1) and L(2,1) labelings for n-cube." Journal of Combinatorial Optimization 28.3 (2014): 626-638.