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Ricci curvature, diameter and eigenvalues of amply regular graphs

Authors :
Chen, Kaizhe
Hu, Chunyang
Liu, Shiping
Zhang, Heng
Publication Year :
2024

Abstract

We prove a weaker version of a conjecture proposed by Qiao, Park and Koolen on diameter bounds of amply regular graphs and make new progress on Terwilliger's conjecture on finiteness of amply regular graphs. We achieve these results by a significantly improved Lin--Lu--Yau curvature estimate and new Bakry--\'Emery curvature estimates. We further discuss applications of our curvature estimates to bounding eigenvalues, isoperimetric constants, and volume growth. In particular, we obtain a volume estimate of amply regular graphs which is sharp for hypercubes.<br />Comment: 32 pages, 2 figures. All comments are welcome!

Details

Database :
arXiv
Publication Type :
Report
Accession number :
edsarx.2410.21055
Document Type :
Working Paper