On the Harmonic characteristic polynomial of specific graphs
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911268675256320 |
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| author | Rahimi, Sadruddin Alikhani, Saeid |
| author_facet | Rahimi, Sadruddin Alikhani, Saeid |
| contents | This paper explores the Harmonic matrix $MH(G)$ associated with a simple graph $ G $, where each entry corresponds to $ \frac{2}{d_i + d_j} $ for adjacent vertices $ v_i $ and $ v_j $. We investigate the spectral properties of this matrix, particularly focusing on its eigenvalues. A central objective of this work is to compute the Harmonic characteristic polynomial. Furthermore, we analyze the Harmonic energy $ HE(G) $ of a graph as the sum of the absolute values of the eigenvalues of $ MH(G) $. Explicit expressions for both the Harmonic characteristic polynomial and the Harmonic energy are derived for several specific classes of graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_12734 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Harmonic characteristic polynomial of specific graphs Rahimi, Sadruddin Alikhani, Saeid Combinatorics 15A18, 05C50 This paper explores the Harmonic matrix $MH(G)$ associated with a simple graph $ G $, where each entry corresponds to $ \frac{2}{d_i + d_j} $ for adjacent vertices $ v_i $ and $ v_j $. We investigate the spectral properties of this matrix, particularly focusing on its eigenvalues. A central objective of this work is to compute the Harmonic characteristic polynomial. Furthermore, we analyze the Harmonic energy $ HE(G) $ of a graph as the sum of the absolute values of the eigenvalues of $ MH(G) $. Explicit expressions for both the Harmonic characteristic polynomial and the Harmonic energy are derived for several specific classes of graphs. |
| title | On the Harmonic characteristic polynomial of specific graphs |
| topic | Combinatorics 15A18, 05C50 |
| url | https://arxiv.org/abs/2511.12734 |