Upper Locating-Domination Numbers of Cycles
Received:November 22, 2009  Revised:April 22, 2011
Key Word: locating-domination number   upper locating-domination number   cycle.  
Fund ProjectL: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 NameAffiliation
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 
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      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.
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