Let G be a non-abelian finite simple group. In addition, let \(\Delta _G\) be the intersection graph of G, whose vertices are the proper non-trivial subgroups of G, with distinct subgroups joined by an edge if and only if they intersect non-trivially. We prove that the diameter of \(\Delta _G\) has a tight upper bound of 5, thereby resolving a question posed by Shen (Czechoslov Math J 60(4):945–950, 2010). Furthermore, a diameter of 5 is achieved only by the baby monster group and certain unitary groups of odd prime dimension.

中文翻译：

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有限简单组的交点图的直径最大为5

令G为非阿贝尔有限简单群。此外，让\（\德尔塔_G \）是交叉点图形ģ，其顶点是适当的非平凡的子组G ^，与由边缘连接当且仅当它们相交的非平凡不同亚组。我们证明\（\ Delta _G \）的直径具有5的严格上限，从而解决了Shen提出的问题（Czechoslov Math J 60（4）：945–950，2010）。此外，只有小怪兽组和某些奇数素数的单一组才能达到5的直径。