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arXiv · 2602.09488

A Combinatorial Proof of Cayley's Formula via Degree Sequences

Helia Karisani·Mohammadreza Daneshvaramoli
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Abstract

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.

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Helia Karisani, Mohammadreza Daneshvaramoli. 2026-02-10. A Combinatorial Proof of Cayley's Formula via Degree Sequences. https://arxiv.org/abs/2602.09488

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