| Title | Notes on L(1,1) and L(2,1) labelings for n -cube |
| Creator | |
| Date Issued | 2014 |
| Source Publication | Journal of Combinatorial Optimization
 |
| ISSN | 1382-6905 |
| Volume | 28 |
| Issue | 3 |
| Pages | 626-638 |
| 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 d(u,v)=1; and |f(u)-f(v)|≥ 1 if d(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, λ(G), is the minimum of span over all L(d,1) -labelings of G. Whittlesey et al. proved that λ (Q)≤ 2+2-2, where n≤ 2-q and 1≤ q≤ k+1. As a consequence, λ(Q)≤ 2n for n≥ 3. In particular, λ (Q)≤ 2-1. In this paper, we provide an elementary proof of this bound. Also, we study the (1,1) -labeling number of Q. A lower bound on λ(Q ) are provided and λ(Q) are determined. © 2012 Springer Science+Business Media New York. |
| Keyword | Channel assignment problem Distance two labeling n -cube |
| DOI | 10.1007/s10878-012-9568-6 |
| URL | View source |
| Language | 英语English |
| Scopus ID | 2-s2.0-84906948383 |
| Citation statistics |
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| Document Type | Conference paper |
| Identifier | http://repository.uic.edu.cn/handle/39GCC9TT/6515 |
| Collection | Beijing Normal-Hong Kong Baptist University |
| Affiliation | 1.Department of Mathematics, Hong Kong Baptist University,224 Waterloo Road,Kowloon Tong,Hong Kong 2.Division of Science and Technology, BNU-HKBU United International College,Zhuhai,China |
| First Author Affilication | Beijing Normal-Hong Kong Baptist University |
| Recommended Citation GB/T 7714 | Zhou，Haiying,Shiu，Wai Chee,Lam，Peter Che Bor. Notes on L(1,1) and L(2,1) labelings for n -cube[C], 2014: 626-638. |
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