TY - GEN

T1 - The Dominant Metric Dimension of Generalized Petersen Graph

AU - Susilowati, Liliek

AU - Mufidah, Izza Wardatul

AU - Estuningsih, Nenik

N1 - Publisher Copyright:
© 2023 American Institute of Physics Inc.. All rights reserved.

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

KW - Resolving set

KW - dominant metric dimension

KW - dominating set

UR - http://www.scopus.com/inward/record.url?scp=85181556078&partnerID=8YFLogxK

U2 - 10.1063/5.0181076

DO - 10.1063/5.0181076

M3 - Conference contribution

AN - SCOPUS:85181556078

T3 - AIP Conference Proceedings

BT - AIP Conference Proceedings

A2 - Pusporani, Elly

A2 - Millah, Nashrul

A2 - Hariyanti, Eva

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 -