The graph zeta functions with respect to the group matrix of a finite group
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915207863861248 |
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| author | Miezaki, Tsuyoshi Sato, Iwao |
| author_facet | Miezaki, Tsuyoshi Sato, Iwao |
| contents | In this paper, we present formulas for the edge zeta function and the second weighted zeta function with respect to the group matrix of a finite abelian group $Γ$. Furthermore, we give another proof of Dedekind Theorem for the group determinant of $Γ$ by the decomposition formula for a matrix of a group covering of a digraph. Finally, we treat the weighted complexity of the complete graph with entries of the group matrix of $Γ$ as arc weights. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_16821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The graph zeta functions with respect to the group matrix of a finite group Miezaki, Tsuyoshi Sato, Iwao Combinatorics 05C50, 15A15 In this paper, we present formulas for the edge zeta function and the second weighted zeta function with respect to the group matrix of a finite abelian group $Γ$. Furthermore, we give another proof of Dedekind Theorem for the group determinant of $Γ$ by the decomposition formula for a matrix of a group covering of a digraph. Finally, we treat the weighted complexity of the complete graph with entries of the group matrix of $Γ$ as arc weights. |
| title | The graph zeta functions with respect to the group matrix of a finite group |
| topic | Combinatorics 05C50, 15A15 |
| url | https://arxiv.org/abs/2503.16821 |