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<p>The spectrum of the Laplacian and the signless Laplacian matrix for a graph product is obtained, where both underlying graphs are regular. As an application of this, we have been able to generate the Kirchhoff Index and Wiener Index and determine the number of spanning trees. Additionally, we derived the conditions necessary for obtaining a Laplacian and a signless Laplacian integral product graph.</p>

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Laplacian polynomial of a graph product and its application

  • 期刊论文

  • 发表日期：

    2026年4月27日

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  • Bishal Sonar,
  • Ravi Srivastava

摘要

The spectrum of the Laplacian and the signless Laplacian matrix for a graph product is obtained, where both underlying graphs are regular. As an application of this, we have been able to generate the Kirchhoff Index and Wiener Index and determine the number of spanning trees. Additionally, we derived the conditions necessary for obtaining a Laplacian and a signless Laplacian integral product graph.