The k -Metric Dimension of a Unicyclic Graph

Alejandro Estrada-Moreno
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Alejandro Estrada-Moreno: Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007 Tarragona, Spain

Mathematics, 2021, vol. 9, issue 21, 1-14

Abstract: Given a connected graph G = ( V ( G ) , E ( G ) ) , a set S ? V ( G ) is said to be a k -metric generator for G if any pair of different vertices in V ( G ) is distinguished by at least k elements of S . A metric generator of minimum cardinality among all k -metric generators is called a k -metric basis and its cardinality is the k -metric dimension of G . We initially present a linear programming problem that describes the problem of finding the k -metric dimension and a k -metric basis of a graph G . Then we conducted a study on the k-metric dimension of a unicyclic graph.

Keywords: unicyclic graph; k -metric generator; k -metric dimension; k -metric dimensional graph; linear programming problem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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