Upper Locating-Domination Numbers of Cycles |
Received:November 22, 2009 Revised:April 22, 2011 |
Key Words:
locating-domination number upper locating-domination number cycle.
|
Fund Project:Supported by the National Natural Science Foundation of China (Grant No.60773078) and the Natural Science Foundation of Anhui Provincial Education Department (No.KJ2011B090). |
Author Name | Affiliation | Yan Cai ZHAO | Foundation Department, Wuxi City College of Vocational Technology, Jiangsu 214153, P. R. China Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China | Er Fang SHAN | Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China | Ru Zhao GAO | Department of Mathematics and Physics, Bengbu College, Anhui 233030, P. R. China |
|
Hits: 2553 |
Download times: 2077 |
Abstract: |
A set $D$ of vertices in a graph $G =(V, E)$ is a locating-dominating set (LDS) if for every two vertices $u,v$ of $V\setminus D$ the sets $N(u)\cap D$ and $N(v)\cap D$ are non-empty and different. The locating-domination number $\gamma_{\rm L}(G)$ is the minimum cardinality of an LDS of $G$, and the upper-locating domination number $\Gamma_{\rm L}(G)$ is the maximum cardinality of a minimal LDS of $G$. In the present paper, methods for determining the exact values of the upper locating-domination numbers of cycles are provided. |
Citation: |
DOI:10.3770/j.issn:1000-341X.2011.04.023 |
View Full Text View/Add Comment |
|
|
|