# Closed Formulae for the Strong Metric Dimension of Lexicographi

• Volume: 36, Issue: 4, page 1051-1064
• ISSN: 2083-5892

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## Abstract

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Given a connected graph G, a vertex w ∈ V (G) strongly resolves two vertices u, v ∈ V (G) if there exists some shortest u − w path containing v or some shortest v − w path containing u. A set S of vertices is a strong metric generator for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong metric generator for G is called the strong metric dimension of G. In this paper we obtain several relationships between the strong metric dimension of the lexicographic product of graphs and the strong metric dimension of its factor graphs.

## How to cite

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Dorota Kuziak, Ismael G. Yero, and Juan A. Rodríguez-Velázquez. "Closed Formulae for the Strong Metric Dimension of Lexicographi." Discussiones Mathematicae Graph Theory 36.4 (2016): 1051-1064. <http://eudml.org/doc/287156>.

@article{DorotaKuziak2016,
abstract = {Given a connected graph G, a vertex w ∈ V (G) strongly resolves two vertices u, v ∈ V (G) if there exists some shortest u − w path containing v or some shortest v − w path containing u. A set S of vertices is a strong metric generator for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong metric generator for G is called the strong metric dimension of G. In this paper we obtain several relationships between the strong metric dimension of the lexicographic product of graphs and the strong metric dimension of its factor graphs.},
author = {Dorota Kuziak, Ismael G. Yero, Juan A. Rodríguez-Velázquez},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {strong metric dimension; strong metric basis; strong metric generator; lexicographic product graphs},
language = {eng},
number = {4},
pages = {1051-1064},
title = {Closed Formulae for the Strong Metric Dimension of Lexicographi},
url = {http://eudml.org/doc/287156},
volume = {36},
year = {2016},
}

TY - JOUR
AU - Dorota Kuziak
AU - Ismael G. Yero
AU - Juan A. Rodríguez-Velázquez
TI - Closed Formulae for the Strong Metric Dimension of Lexicographi
JO - Discussiones Mathematicae Graph Theory
PY - 2016
VL - 36
IS - 4
SP - 1051
EP - 1064
AB - Given a connected graph G, a vertex w ∈ V (G) strongly resolves two vertices u, v ∈ V (G) if there exists some shortest u − w path containing v or some shortest v − w path containing u. A set S of vertices is a strong metric generator for G if every pair of vertices of G is strongly resolved by some vertex of S. The smallest cardinality of a strong metric generator for G is called the strong metric dimension of G. In this paper we obtain several relationships between the strong metric dimension of the lexicographic product of graphs and the strong metric dimension of its factor graphs.
LA - eng
KW - strong metric dimension; strong metric basis; strong metric generator; lexicographic product graphs
UR - http://eudml.org/doc/287156
ER -

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