@article{dc4b8a79a15147c9bb77cbfa51e6a99c, title = "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 ΔG 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 ΔG 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.", keywords = "Intersection graph, Simple group, Subgroups", author = "Freedman, {Saul D.}", note = "The author was supported by a St Leonard{\textquoteright}s International Doctoral Fees Scholarship and a School of Mathematics & Statistics PhD Funding Scholarship at the University of St Andrews.", year = "2021", month = feb, day = "13", doi = "10.1007/s00013-021-01583-3", language = "English", volume = "First Online", journal = "Archiv der Mathematik", issn = "0003-889X", publisher = "Birkhauser Verlag Basel", }