We construct distance-regular graphs, including strongly regular graphs, admitting a transitive action of the Chevalley groups \(G_2(4)\) and \(G_2(5)\), the orthogonal group O(7, 3) and the Tits group \(T=\)\(^2F_4(2)'\). Most of the constructed graphs have more than 1000 vertices, and the number of vertices goes up to 28431. Some of the obtained graphs are new.

中文翻译：

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在一些具有许多顶点的距离正则图上

我们构造距离正则图，包括强正则图，并接受Chevalley群\（G_2（4）\）和\（G_2（5）\），正交群O（7，3）和Tits的传递作用组\（T = \）\（^ 2F_4（2）'\）。大多数构造的图具有超过1000个顶点，并且顶点数高达28431。获得的一些图是新的。