| 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 |
|
|
|
