Characterizing the Degree-Kirchhoff, Gutman, and Schultz Indices in Pentagonal Cylinders and Möbius Chains
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866914941969104896 |
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| author | Sahir, Md. Abdus Nayeem, Sk. Md. Abu |
| author_facet | Sahir, Md. Abdus Nayeem, Sk. Md. Abu |
| contents | The degree-Kirchhoff index of a connected graph is defined as the sum 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 formulations for the degree-Kirchhoff index of various kinds of class graphs. This paper presents closed-form formulas for the degree-Kirchhoff index of pentagonal cylinders and Möbius chains. Additionally, we calculate the Gutman index and Schultz index for these graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_07170 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Characterizing the Degree-Kirchhoff, Gutman, and Schultz Indices in Pentagonal Cylinders and Möbius Chains Sahir, Md. Abdus Nayeem, Sk. Md. Abu Combinatorics Discrete Mathematics Primary: 05C09, 05C12, Secondary: 05C50 The degree-Kirchhoff index of a connected graph is defined as the sum 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 formulations for the degree-Kirchhoff index of various kinds of class graphs. This paper presents closed-form formulas for the degree-Kirchhoff index of pentagonal cylinders and Möbius chains. Additionally, we calculate the Gutman index and Schultz index for these graphs. |
| title | Characterizing the Degree-Kirchhoff, Gutman, and Schultz Indices in Pentagonal Cylinders and Möbius Chains |
| topic | Combinatorics Discrete Mathematics Primary: 05C09, 05C12, Secondary: 05C50 |
| url | https://arxiv.org/abs/2302.07170 |