Unique Metro Domination of a Ladder

A dominating set $D$ of a graph $G$ which is also a resolving set of $G$ is called a metro dominating set. A metro dominating set $D$ of a graph $G(V,E)$ is a unique metro dominating set (in short an UMD-set) if $|N(v) \cap D| = 1$ for each vertex $v\in V-D$ and the minimum cardinality of an UMD-set...

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Bibliographic Details
Published in:Mapana Journal of Sciences 2016-07, Vol.15 (3), p.55-64
Main Authors: Sherra, John, Sooryanarayana, Badekara
Format: Article
Language:English
Online Access:Get full text
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Summary:A dominating set $D$ of a graph $G$ which is also a resolving set of $G$ is called a metro dominating set. A metro dominating set $D$ of a graph $G(V,E)$ is a unique metro dominating set (in short an UMD-set) if $|N(v) \cap D| = 1$ for each vertex $v\in V-D$ and the minimum cardinality of an UMD-set of $G$ is the unique metro domination number of $G$. In this paper, we determine unique metro domination number of $P_n\times P_2$.
ISSN:0975-3303
0975-3303
DOI:10.12723/mjs.38.6