R-Sets and Metric Dimension of Necklace Graphs

Authors

Ioan Tomescu, Faculty of Mathematics and Informatics, University of Bucharest, Str. Academiei, 14, 010014 Bucharest, Romania\\ dus Salam School of Mathematical Sciences, GC University Lahore, 68-B, New Muslim Town, Lahore, PakistanFollow
Muhammad Imran, Department of Mathematics, School of Natural Sciences, National University of Sciences and Technology, Sector H-12, Islamabad, PakistanFollow

Author Country (or Countries)

Pakistan

Abstract

The R-set relative to a pair of distinct vertices of a connected graph G is the set of vertices whose distances to these vertices are distinct. In this paper R-sets are used to show that metric dimension dim(Nen) = 3 when n is odd and 2 otherwise, where Nen is the necklace graph of order 2n+2. It is also shown that the exchange property of the bases in a vector space does not hold for minimal resolving sets of Nen if n is even.

Digital Object Identifier (DOI)

http://dx.doi.org/10.12785/amis/090109

Recommended Citation

Tomescu, Ioan and Imran, Muhammad (2023) "R-Sets and Metric Dimension of Necklace Graphs," Applied Mathematics & Information Sciences: Vol. 09: Iss. 1, Article 16.
DOI: http://dx.doi.org/10.12785/amis/090109
Available at: https://digitalcommons.aaru.edu.jo/amis/vol09/iss1/16