Metric Locations in Pseudotrees: A Survey and New Results

José Cáceres () and Ignacio M. Pelayo
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José Cáceres: Departamento de Matemáticas, Universidad de Almería, ctra. Sacramento s/n, 04120 Almería, Spain
Ignacio M. Pelayo: Departament of Matemàtiques, Universitat Politècnica de Catalunya, c/Esteve Terradas nº8, 08860 Castelldefels, Spain

Mathematics, 2025, vol. 13, issue 4, 1-28

Abstract: This paper presents a comprehensive review of the literature on the original concept of metric location, along with its various adaptations and extensions that have been developed over time. Given that determining a minimum location set is generally NP-hard, we focus on analyzing the behavior of these sets within specific graph families, including paths, cycles, trees and unicyclic graphs. In addition to synthesizing existing knowledge, we contribute new findings and insights to the field, advancing the understanding of metric location problems in these structured graph classes.

Keywords: metric dimension; metric locating sets; distance in graphs; unicyclic graphs (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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