<p>Graphs with an ideally restricted spectrum are known as Ramanujan graphs. In computer science and combinatorics, these graphs have several uses. This paper explores the metric dimension of Ramanujan graphs. Metric dimension is the minimum “Locator points” needed to uniquely locate every spot in a network. Ramanujan graphs are highly efficient and well-connected networks. Our research investigates how their unique mathematical properties influence this “Locator points” requirement, a problem typically very complex. By using their inherent design, this work aims to understand these networks better and show their potential for precise location-finding in large systems. General codes for these graphs have also been discussed.</p>

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Metric Dimension and General Codes of Ramanujan Graphs

  • Sahil Sharma,
  • Vijay Kumar Bhat

摘要

Graphs with an ideally restricted spectrum are known as Ramanujan graphs. In computer science and combinatorics, these graphs have several uses. This paper explores the metric dimension of Ramanujan graphs. Metric dimension is the minimum “Locator points” needed to uniquely locate every spot in a network. Ramanujan graphs are highly efficient and well-connected networks. Our research investigates how their unique mathematical properties influence this “Locator points” requirement, a problem typically very complex. By using their inherent design, this work aims to understand these networks better and show their potential for precise location-finding in large systems. General codes for these graphs have also been discussed.