The Dominant Metric Dimension of Generalized Petersen Graph

Liliek Susilowati; Izza Wardatul Mufidah; Nenik Estuningsih

doi:10.1063/5.0181076

The Dominant Metric Dimension of Generalized Petersen Graph

Liliek Susilowati, Izza Wardatul Mufidah, Nenik Estuningsih

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

1 Citation (Scopus)

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 language	English
Title of host publication	AIP Conference Proceedings
Editors	Elly Pusporani, Nashrul Millah, Eva Hariyanti
Publisher	American Institute of Physics Inc.
Edition	1
ISBN (Electronic)	9780735447738
DOIs	https://doi.org/10.1063/5.0181076
Publication status	Published - 22 Dec 2023
Event	International Conference on Mathematics, Computational Sciences, and Statistics 2022, ICoMCoS 2022 - Hybrid, Surabaya, Indonesia Duration: 2 Oct 2022 → 3 Oct 2022

Publication series

Name	AIP Conference Proceedings
Number	1
Volume	2975
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	International Conference on Mathematics, Computational Sciences, and Statistics 2022, ICoMCoS 2022
Country/Territory	Indonesia
City	Hybrid, Surabaya
Period	2/10/22 → 3/10/22

Keywords

Generalized Petersen graph
Resolving set
dominant metric dimension
dominating set

Access to Document

10.1063/5.0181076

Cite this

@inproceedings{5c5d2d687a3f4840b7a49e93857c6c47,

title = "The Dominant Metric Dimension of Generalized Petersen Graph",

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.",

keywords = "Generalized Petersen graph, Resolving set, dominant metric dimension, dominating set",

author = "Liliek Susilowati and Mufidah, {Izza Wardatul} and Nenik Estuningsih",

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year = "2023",

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Susilowati, L, Mufidah, IW & Estuningsih, N 2023, The Dominant Metric Dimension of Generalized Petersen Graph. in E Pusporani, N Millah & E Hariyanti (eds), AIP Conference Proceedings. 1 edn, 020005, AIP Conference Proceedings, no. 1, vol. 2975, American Institute of Physics Inc., International Conference on Mathematics, Computational Sciences, and Statistics 2022, ICoMCoS 2022, Hybrid, Surabaya, Indonesia, 2/10/22. https://doi.org/10.1063/5.0181076

The Dominant Metric Dimension of Generalized Petersen Graph. / Susilowati, Liliek; Mufidah, Izza Wardatul; Estuningsih, Nenik.
AIP Conference Proceedings. ed. / Elly Pusporani; Nashrul Millah; Eva Hariyanti. 1. ed. American Institute of Physics Inc., 2023. 020005 (AIP Conference Proceedings; Vol. 2975, No. 1).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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T1 - The Dominant Metric Dimension of Generalized Petersen Graph

AU - Susilowati, Liliek

AU - Mufidah, Izza Wardatul

AU - Estuningsih, Nenik

PY - 2023/12/22

Y1 - 2023/12/22

N2 - 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.

AB - 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.

KW - Generalized Petersen graph

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KW - dominating set

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PB - American Institute of Physics Inc.

T2 - International Conference on Mathematics, Computational Sciences, and Statistics 2022, ICoMCoS 2022

Y2 - 2 October 2022 through 3 October 2022

ER -

The Dominant Metric Dimension of Generalized Petersen Graph

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Keywords

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