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<p>For a connected graph, the degree-Kirchhoff index is the aggregate of the reciprocals of the non-zero eigenvalues of the normalized Laplacian matrix, each multiplied by the graph’s total degree. Several studies have recently obtained explicit forms of the degree-Kirchhoff index of various kinds of graphs. This paper deals with cylinder chains and Möbius chains formed by pentagons. Expressions for the degree-Kirchhoff index of those graphs are found in terms of the number of pentagons. In addition, we find the Gutman and Schultz indices for them.</p>

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Characterizing the Degree-Kirchhoff, Gutman, and Schultz Indices in Pentagonal Cylinders and Möbius Chains

  • 期刊论文

  • 发表日期：

    2025年5月15日

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  • Md. Abdus Sahir,
  • Sk. Md. Abu Nayeem

摘要

For a connected graph, the degree-Kirchhoff index is the aggregate of the reciprocals of the non-zero eigenvalues of the normalized Laplacian matrix, each multiplied by the graph’s total degree. Several studies have recently obtained explicit forms of the degree-Kirchhoff index of various kinds of graphs. This paper deals with cylinder chains and Möbius chains formed by pentagons. Expressions for the degree-Kirchhoff index of those graphs are found in terms of the number of pentagons. In addition, we find the Gutman and Schultz indices for them.