A1 Refereed original research article in a scientific journal
On Stronger Types of Locating-Dominating Codes
Authors: Ville Junnila, Tero Laihonen, Tuomo Lehtilä, María Luz Puertas
Publisher: DISCRETE MATHEMATICS THEORETICAL COMPUTER SCIENCE
Publication year: 2019
Journal: Discrete Mathematics and Theoretical Computer Science
Journal acronym: DISCRETE MATH THEOR
Article number: UNSP 1
Volume: 21
Issue: 1
Number of pages: 21
ISSN: 1462-7264
eISSN: 1365-8050
Web address : https://dmtcs.episciences.org/5344
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/42457173
Locating-dominating codes in a graph find their application in sensor networks and have been studied extensively over the years. A locating-dominating code can locate one object in a sensor network, but if there is more than one object, it may lead to false conclusions. In this paper, we consider stronger types of locating-dominating codes which can locate one object and detect if there are multiple objects. We study the properties of these codes and provide bounds on the smallest possible size of these codes, for example, with the aid of the Dilworth number and Sperner families Moreover, these codes are studied in trees and Cartesian products of graphs. We also give the complete realization theorems for the coexistence of the smallest possible size of these codes and the optimal locating-dominating codes in a graph.
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