Weighted sums of rooted spanning forests on cycles with pendant edges
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929240780308480 |
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| author | Fujita, Hajime Hasegawa, Kimiko Inaba, Yukie Kondo, Takefumi |
| author_facet | Fujita, Hajime Hasegawa, Kimiko Inaba, Yukie Kondo, Takefumi |
| contents | We derive two formulas for the weighted sums of rooted spanning forests of particular sequence of graphs by using the matrix tree theorem. We consider cycle graphs with edges so called the pendant edges. One of our formula can be described as a variable transformation of the Chebyshev polynomial. They have particular algebraic properties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07209 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Weighted sums of rooted spanning forests on cycles with pendant edges Fujita, Hajime Hasegawa, Kimiko Inaba, Yukie Kondo, Takefumi Combinatorics Rings and Algebras 05C30, 05C50 We derive two formulas for the weighted sums of rooted spanning forests of particular sequence of graphs by using the matrix tree theorem. We consider cycle graphs with edges so called the pendant edges. One of our formula can be described as a variable transformation of the Chebyshev polynomial. They have particular algebraic properties. |
| title | Weighted sums of rooted spanning forests on cycles with pendant edges |
| topic | Combinatorics Rings and Algebras 05C30, 05C50 |
| url | https://arxiv.org/abs/2402.07209 |