English

Distance-regular graph with large a1 or c2

Combinatorics 2010-08-09 v1

Abstract

In this paper, we study distance-regular graphs Γ\Gamma 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\Gamma. 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.

Keywords

Cite

@article{arxiv.1008.1209,
  title  = {Distance-regular graph with large a1 or c2},
  author = {Jack H. Koolen and Jongyook Park},
  journal= {arXiv preprint arXiv:1008.1209},
  year   = {2010}
}

Comments

We submited this manuscript to JCTA

R2 v1 2026-06-21T15:57:56.511Z