Resolving-power dominating sets

Journal article

Stephen, Sudeep, Rajan, Bharati, Grigorious, Cyriac and William, Albert. (2015). Resolving-power dominating sets. Applied Mathematics and Computation. 256, pp. 778-785. https://doi.org/10.1016/j.amc.2015.01.037
AuthorsStephen, Sudeep, Rajan, Bharati, Grigorious, Cyriac and William, Albert
Abstract

For a graph G(V,E) that models a facility or a multi-processor network, detection devices can be placed at vertices so as to identify the location of an intruder such as a thief or fire or saboteur or a faulty processor. Resolving-power dominating sets are of interest in electric networks when the latter helps in the detection of an intruder/fault at a vertex. We define a set S ⊆ V to be a resolving-power dominating set of G if it is resolving as well as a power-dominating set. The minimum cardinality of S is called resolving-power domination number. In this paper, we show that the problem is NP-complete for arbitrary graphs and that it remains NP-complete even when restricted to bipartite graphs. We provide lower bounds for the resolving-power domination number for trees and identify classes of trees that attain the lower bound. We also solve the problem for complete binary trees.

KeywordsDomination; Power domination; Metric dimension
Year01 Jan 2015
JournalApplied Mathematics and Computation
Journal citation256, pp. 778-785
PublisherAcademic Press (Elsevier)
ISSN0096-3003
Digital Object Identifier (DOI)https://doi.org/10.1016/j.amc.2015.01.037
Web address (URL)https://www.sciencedirect.com/science/article/pii/S009630031500051X?via%3Dihub
Research or scholarlyResearch
Page range778-785
Publisher's version
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All rights reserved
File Access Level
Controlled
Output statusPublished
Publication dates
Print01 Apr 2015
Online15 Feb 2015
Publication process dates
Deposited22 May 2024
Additional information

© 2015 Elsevier Inc. All rights reserved.

Place of publicationUnited States
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