A Combinatorial Proof of Cayley's Formula via Degree Sequences

arXiv (Cornell University) 2026 Preprint Open access

Read full text
Authors: Helia Karisani, Mohammadreza Daneshvaramoli
DOI: 10.48550/arxiv.2602.09488
Cited by: 0

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.

Fields of Study & Subjects

Advanced Combinatorial Mathematics Advanced Graph Theory Research Limits and Structures in Graph Theory

Publication details

Journal / source
arXiv (Cornell University)
Publication date
10 February 2026
Language
EN
Document type
Preprint