In this note we investigate how to use an initial portion of the intersection array of a distance-regular graph to give an upper bound for the diameter of the graph. We prove three new diameter bounds. Our bounds are tight for the Hamming d-cube, doubled Odd graphs, the Heawood graph, Tutte’s 8-cage and 12-cage, the generalized dodecagons of order (1, 3) and (1, 4), the Biggs-Smith graph, the Pappus graph, the Wells graph, and the dodecahedron.

中文翻译：

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关于距离-正则图的直径的有界

在本笔记中，我们研究如何使用距离正则图的交集数组的初始部分来给出图直径的上限。我们证明了三个新的直径界限。我们的边界对于汉明d立方体、双奇数图、希伍德图、Tutte 的 8 笼和 12 笼、阶 (1, 3) 和 (1, 4) 的广义十二边形、Biggs-Smith 图是严格的、Pappus 图、Wells 图和十二面体。