Distance-regular graph with large a1 or c2

2010/08/06 by Jack H. Koolen, Koolen, Jack H., Jongyook Park +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems #math.CO

paper · pdf · doi:10.48550/arxiv.1008.1209

We submited this manuscript to JCTA

arxiv created 2010/08/06 · openalex publication_date 2010/08/06 · arxiv updated 2010/08/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study distance-regular graphs Γ that have a pair of distinct vertices, say x and y, such that the number of common neighbors of x and y is about half the valency of Γ. We show that if the diameter is at least three, then such a graph, besides a finite number of exceptions, is a Taylor graph, bipartite with diameter three or a line graph.

Citations

• An inequality involving the second largest and smallest eigenvalue of a distance-regular graph

Related

• There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k2/k and large diameter
• A relationship between the diameter and the intersection number c2 for a distance-regular graph
• The least Euclidean distortion constant of a distance-regular graph
• The metric dimension of small distance-regular and strongly regular graphs
• Distance-regular graphs without 4-claws