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Metric Dimension of Some Generalized Families of Toeplitz Graphs

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  • Muhammad Faisal Nadeem
  • Shaojian Qu
  • Ali Ahmad
  • Muhammad Azeem
  • Akif Akgul

Abstract

The metric dimension of a graph G is the selection of the minimum possible number of vertices such that each vertex of the graph G is distinctively defined by its vector of distances to the set of selected vertices. It was proved that the problem of determining the metric dimension of a graph is NP-hard. In this paper, the metric dimension of Toeplitz graphs with two and three generators is discussed and the exact values are found. Also, two conjectures about the exact metric dimension of Toeplitz graphs are given.

Suggested Citation

  • Muhammad Faisal Nadeem & Shaojian Qu & Ali Ahmad & Muhammad Azeem & Akif Akgul, 2022. "Metric Dimension of Some Generalized Families of Toeplitz Graphs," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-10, March.
    • Handle: RePEc:hin:jnlmpe:9155291
    DOI: 10.1155/2022/9155291
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