Central Metric Dimension of Rooted Product Graph

  • Liliek Susilowati Department of Mathematics Universitas Airlangga
  • Nenik Estuningsih Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga
  • Tyas Widya Damayanti Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga
  • Muchammad Yusuf Saifuddin Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga
  • Bustomi Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga
  • Fadekemi Janet Osaye Department of Mathematics and Statistics, Troy University, Alabama
DOI: https://doi.org/10.19139/soic-2310-5070-2156
Keywords: radius; central set; central resolving set; rooted product graph; central metric dimension.

Abstract

The Central metric dimension is a type of metric dimension on graph. Some special graphs for which the central metric dimension have been found include path graph, cycle graph, complete graph, and complete bipartite graph. The aim of this study is to determine the central metric dimension of rooted product graph. Let G  be a connected graph of order n and H is a sequence of  n rooted graphs H1, H2, H3, ..., Hn . The rooted product graph  G and H denoted by GoH . In this paper, we determine the central metric dimension of rooted product graph  which denoted by dimcen( GoH). The results obtained for GoH  where H is a sequence of rooted graphs that all have the same radius and the rooted vertex is the central vertex. For H is a sequence of rooted cycle graph, the cycle with the largest radius has an impact on the central set, while the central metric dimension is affected by the central set of GoH . For H  is a sequence of rooted complete graph, the central set is affected by the central set of a graph G, while the central metric dimension is affected by the central set of the graph G.

Author Biographies

Nenik Estuningsih, Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga
Department of Mathematics
Tyas Widya Damayanti, Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga
epartment of Mathematics
Muchammad Yusuf Saifuddin, Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga
Department of Mathematics
Bustomi, Department of Mathematics, Faculty of Science and Technology, Universitas Airlangga
Department of Mathematics
Fadekemi Janet Osaye, Department of Mathematics and Statistics, Troy University, Alabama
Department of Mathematics and Statistics
Published
2024-10-18
How to Cite
Liliek Susilowati, Estuningsih, N., Widya Damayanti, T., Yusuf Saifuddin, M., Bustomi, & Janet Osaye, F. (2024). Central Metric Dimension of Rooted Product Graph. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2156
Issue
Online First
Section
Research Articles
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