Distance-regular graph with large a1 or c2

Details Distance-regular graph with large a1 or c2 Distance-regular graph with large a1 or c2

2010-08-06

arxiv.org/abs/1008.1209v1

Mathematics

Combinatorics

We submited this manuscript to JCTA

Scientific paper

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.

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