On the central resolver set of the edge coronation graphs

Susilowati, Liliek; Slamin, Slamin; Maulida, Utik; Estuningsih, Nenik; Zahidah, Siti; Prabhu, S.

doi:10.47974/JDMSC-1819

Open Access Research Article

On the central resolver set of the edge coronation graphs

^*Liliek SusilowatiCorresponding authorliliek-s@fst.unair.ac.idDepartment of Mathematics Faculty of Science and Technology Universitas AirlanggaSurabaya, 60115, IndonesiaView full profile → , Slamin Slaminslamin@unej.ac.idStudy Program of Informatics Faculty of Computer Science Universitas JemberDepartment of Computer Sciences Universitas JemberJember, 68121, IndonesiaView full profile → , Utik Maulidautik.maulida-2018@fst.unair.ac.idDepartment of Mathematics Faculty of Science and Technology Universitas AirlanggaSurabaya, 60115, IndonesiaView full profile → , Nenik Estuningsihnenik-e@fst.unair.ac.idDepartment of Mathematics Faculty of Science and Technology Universitas AirlanggaSurabaya, 60115, IndonesiaView full profile → , Siti Zahidahsiti.zahidah@fst.unair.ac.idDepartment of Mathematics Faculty of Science and Technology Universitas AirlanggaSurabaya, 60115, IndonesiaView full profile → , S. Prabhudrsavariprabhu@gmail.comDepartment of Mathematics Rajalakshmi Engineering College (Autonomous) Department of Mathematics Rajalakshmi Engineering CollegeChennai, Tamil Nadu, 602105, IndiaView full profile →

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pp. 29–42Vol. 28Issue 1February 2025DOI: 10.47974/JDMSC-1819 Crossmark XML

Received:: 14 Dec 2022
Published Online:: 28 Feb 2025
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1819
Pages:: 29–42

Abstract

Graph theory as part of mathematics, has experienced significant development from the theoretical aspect, one of it is the theory of metric dimension. The concept of metric dimensions has evolved greatly, including the dominant metric dimension and the complement metric dimension. In this study, the concept of the central metric dimension is introduced, that is a combination of the metric dimension and central of a graph. The minimum number of vertices of a resolver set that contains a central set is called the central metric dimension of graph G, and denoted by dimcen(G). Several characterizations of a graph having a certain central metric dimension are yielded in this study. Several relations are obtained between the central metric dimension and the metric dimension. Furthermore, the central metric dimension is applied on edge coronation graphs. The edge coronation of graphs G and H is denoted by (G ◊ H). The results of the study show that the central metric dimension of edge coronation of G and H are influenced by the central set and the order of graph G and the metric dimension of graph H.

Keywords

Graph Metric dimension Central metric dimension Accessible transportation Edge coronation graphs

Subject Classifications

05C1205C7505C38

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