The Dominant Metric Dimension of Generalized Petersen Graph

Liliek Susilowati, Izza Wardatul Mufidah, Nenik Estuningsih

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

The dominant metric dimension is the development of the concepts of the resolving set and the dominating set of graphs. In this research, the dominant metric dimension concept is applied to a generalize Petersen graph. The purpose of this research is to determine the dominant metric dimension of a generalized Petersen graph. The dominant metric dimension is the minimum cardinality of the dominant resolving set. The dominant metric dimension of a generalized Petersen graph is denoted by Ddim(P(n, k)) for natural number n, k where n > 2k. The minimum cardinality of dominating set of the graph G is called a dominating number of G, denoted by y(G). The results of this research are the dominant metric dimension of the generalized Petersen graph Ddim(P(n, i)) = y(P(n, i)) for i = {1,2} and Ddim(P(n, 3)) = y(P(n, 3)) + 1 for n 8,14,20 (mod 24) and Ddim(P(n, 3)) = y(P(n, 3)) for other n.

Original languageEnglish
Title of host publicationAIP Conference Proceedings
EditorsElly Pusporani, Nashrul Millah, Eva Hariyanti
PublisherAmerican Institute of Physics Inc.
Edition1
ISBN (Electronic)9780735447738
DOIs
Publication statusPublished - 22 Dec 2023
EventInternational Conference on Mathematics, Computational Sciences, and Statistics 2022, ICoMCoS 2022 - Hybrid, Surabaya, Indonesia
Duration: 2 Oct 20223 Oct 2022

Publication series

NameAIP Conference Proceedings
Number1
Volume2975
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Conference

ConferenceInternational Conference on Mathematics, Computational Sciences, and Statistics 2022, ICoMCoS 2022
Country/TerritoryIndonesia
CityHybrid, Surabaya
Period2/10/223/10/22

Keywords

  • Generalized Petersen graph
  • Resolving set
  • dominant metric dimension
  • dominating set

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