A Combinatorial Proof of Cayley's Formula via Degree Sequences
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914318794096640 |
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| author | Karisani, Helia Daneshvaramoli, Mohammadreza |
| author_facet | Karisani, Helia Daneshvaramoli, Mohammadreza |
| contents | Cayley's formula is a fundamental result in combinatorics that counts the number of labeled trees on n vertices. While existing proofs use approaches such as Prufer sequences and the Matrix-Tree Theorem, we give a combinatorial proof that highlights the role of degree sequences and structural properties of labeled trees. Our goal is to provide an accessible perspective and suggest connections to related enumeration problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_09488 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Combinatorial Proof of Cayley's Formula via Degree Sequences Karisani, Helia Daneshvaramoli, Mohammadreza Combinatorics 05C05 Cayley's formula is a fundamental result in combinatorics that counts the number of labeled trees on n vertices. While existing proofs use approaches such as Prufer sequences and the Matrix-Tree Theorem, we give a combinatorial proof that highlights the role of degree sequences and structural properties of labeled trees. Our goal is to provide an accessible perspective and suggest connections to related enumeration problems. |
| title | A Combinatorial Proof of Cayley's Formula via Degree Sequences |
| topic | Combinatorics 05C05 |
| url | https://arxiv.org/abs/2602.09488 |