On Distance-Regular Graphs with Smallest Eigenvalue at Least -m

2009/08/14 by Jack H. Koolen, J. H. Koolen, Koolen, J. H. +3 · 1 citation
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Finite Group Theory Research #graph theory and CDMA systems #math.CO #math.SP #msc:05C50 #msc:05C75 #msc:05E30

paper · pdf · doi:10.48550/arxiv.0908.2017

arxiv created 2009/08/14 · arxiv updated 2009/12/01

Abstract

A non-complete geometric distance-regular graph is the point graph of a partial geometry in which the set of lines is a set of Delsarte cliques. In this paper, we prove that for fixed integer m≥ 2, there are only finitely many non-geometric distance-regular graphs with smallest eigenvalue at least -m, diameter at least three and intersection number c₂ ≥ 2.

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• An improved bound for strongly regular graphs with smallest eigenvalue -m

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