# Closed Formulae for the Strong Metric Dimension of Lexicographi

Dorota Kuziak; Ismael G. Yero; Juan A. Rodríguez-Velázquez

Discussiones Mathematicae Graph Theory (2016)

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

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topDorota 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 -