The intersection graph of a finite simple group has diameter at most 5
Abstract
Let G be a non-abelian finite simple group. In addition, let G be the intersection graph of G, whose vertices are the proper nontrivial subgroups of G, with distinct subgroups joined by an edge if and only if they intersect nontrivially. We prove that the diameter of G has a tight upper bound of 5, thereby resolving a question posed by Shen (2010). Furthermore, a diameter of 5 is achieved only by the baby monster group and certain unitary groups of odd prime dimension.
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