Shilla distance-regular graphs

2009/02/23 by Jack H. Koolen, Koolen, Jack H., Jongyook Park +1
Computer Science · Engineering · Mathematics · #05E30 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.0902.3860

openalex publication_date 2009/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A Shilla distance-regular graph G (say with valency k) is a distance-regular graph with diameter 3 such that its second largest eigenvalue equals to a3. We will show that a3 divides k for a Shilla distance-regular graph G, and for G we define b=b(G):=k/a3. In this paper we will show that there are finitely many Shilla distance-regular graphs G with fixed b(G)>=2. Also, we will classify Shilla distance-regular graphs with b(G)=2 and b(G)=3. Furthermore, we will give a new existence condition for distance-regular graphs, in general.

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