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arxiv: 1008.1209 · v1 · pith:HTZ2GT7Fnew · submitted 2010-08-06 · 🧮 math.CO

Distance-regular graph with large a1 or c2

classification 🧮 math.CO
keywords graphdiameterdistance-regulargammanumberthreebesidesbipartite
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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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