A structure theory for regular graphs with fixed smallest eigenvalue

Qianqian Yang; Jack H. Koolen

A structure theory for regular graphs with fixed smallest eigenvalue

Combinatorics 2024-01-22 v1

Authors: Qianqian Yang , Jack H. Koolen

Abstract

In this paper we will give a structure theory for regular graphs with fixed smallest eigenvalue. As a consequence of this theory, we show that a $k$ -regular graph with smallest eigenvalue $-\lambda$ has clique number linear in $k$ if $k$ is large with respect to $\lambda$ .

Keywords

graph laplacian graph theory spectral graph theory

Cite

@article{arxiv.2401.10468,
  title  = {A structure theory for regular graphs with fixed smallest eigenvalue},
  author = {Qianqian Yang and Jack H. Koolen},
  journal= {arXiv preprint arXiv:2401.10468},
  year   = {2024}
}

Comments

arXiv admin note: text overlap with arXiv:2011.11935

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