Recent progress on graphs with fixed smallest eigenvalue
Combinatorics
2020-11-25 v1
Abstract
We give a survey on graphs with fixed smallest eigenvalue, especially on graphs with large minimal valency and also on graphs with good structures. Our survey mainly consists of the following two parts: (i) Hoffman graphs, the basic theory related to Hoffman graphs and the applications of Hoffman graphs to graphs with fixed smallest eigenvalue and large minimal valency; (ii) recent results on distance-regular graphs and co-edge regular graphs with fixed smallest eigenvalue and the characterizations of certain families of distance-regular graphs. At the end of the survey, we also discuss signed graphs with fixed smallest eigenvalue and present some new findings.
Keywords
Cite
@article{arxiv.2011.11935,
title = {Recent progress on graphs with fixed smallest eigenvalue},
author = {Jack H. Koolen and Meng-Yue Cao and Qianqian Yang},
journal= {arXiv preprint arXiv:2011.11935},
year = {2020}
}