English

Unsolved Problems in Spectral Graph Theory

Combinatorics 2025-10-16 v3

Abstract

Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and eigenvectors of matrices associated with graphs to study them. In this paper, we present a collection of 2020 topics in spectral graph theory, covering a range of open problems and conjectures. Our focus is primarily on the adjacency matrix of graphs, and for each topic, we provide a brief historical overview.

Keywords

Cite

@article{arxiv.2305.10290,
  title  = {Unsolved Problems in Spectral Graph Theory},
  author = {Lele Liu and Bo Ning},
  journal= {arXiv preprint arXiv:2305.10290},
  year   = {2025}
}

Comments

v3, 30 pages, 1 figure, include comments from Clive Elphick, Xiaofeng Gu, William Linz, and Dragan Stevanovi\'c, respectively. Thanks! This paper will be published in Operations Research Transactions

R2 v1 2026-06-28T10:37:13.164Z