On Metric Dimension of Edge Comb Product of Symmetric Graphs

Authors

  • Tita Khalis Maryati UIN Syarif Hidayatullah Jakarta
  • Dindin Sobiruddin UIN Syarif Hidayatullah Jakarta
  • Fawwaz Fakhrurrozi Hadiputra School of Mathematics and Statistics, The University of Melbourne.

DOI:

https://doi.org/10.25077/jmua.13.4.349-357.2024

Keywords:

Edge Comb Product, Symmetric, Metric Dimension

Abstract

Consider a finite graph G that is simple, undirected, and connected. Let W be an ordered set of vertices with |W| = k. The representation of a vertex v is defined as an ordered k-tuple that consists of the distances from vertex v to each vertex in W. The set W is called a resolving set for G if the k-tuples for any two vertices in G are distinct. The metric dimension of G, denoted by dim(G), is the smallest possible size of such a set W. In this paper, we determine the metric dimension of edge comb product of trees with complete multipartites or petersen graphs.

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Published

31-10-2024

Issue

Vol. 13 No. 4 (2024)

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Articles

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