Distance-regular graph with large a1 or c2

Abstract

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

We submited this manuscript to JCTA

Cited by in corpus (2)

• There are only finitely many distance-regular graphs with valency k at least three, fixed ratio k2/k and large diameter
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