On the local metric dimension of corona product graphs

A vertex \(v\in V(G)\) is said to distinguish two vertices \(x,y\in V(G)\) of a nontrivial connected graph \(G\) if the distance from \(v\) to \(x\) is different from the distance from \(v\) to \(y\). A set \(S\subset V(G)\) is a local metric generator for \(G\) if every two adjacent vertices of \(G...

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Bibliographic Details
Published inarXiv.org
Main Authors Rodriguez-Velazquez, Juan A, Barragan-Ramirez, Gabriel A, Carlos Garcia Gomez
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 16.02.2016
Subjects
Apexes
Graph theory
Graphs
Mathematics - Combinatorics
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Summary:A vertex \(v\in V(G)\) is said to distinguish two vertices \(x,y\in V(G)\) of a nontrivial connected graph \(G\) if the distance from \(v\) to \(x\) is different from the distance from \(v\) to \(y\). A set \(S\subset V(G)\) is a local metric generator for \(G\) if every two adjacent vertices of \(G\) are distinguished by some vertex in \(S\). A local metric generator with the minimum cardinality is called a local metric basis for \(G\) and its cardinality, the local metric dimension of G. In this paper we study the problem of finding exact values for the local metric dimension of corona product of graphs.
ISSN:2331-8422
DOI:10.48550/arxiv.1308.6689