Geodesic
Finite almost simple groups with prime graphs all of whose connected components are cliques
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 132-141

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We find finite almost simple groups with prime graphs all of whose connected components are cliques, i.e., complete graphs. The proof is based on the following fact, which was obtained by the authors and is of independent interest: the prime graph of a finite simple nonabelian group contains two nonadjacent odd vertices that do not divide the order of the outer automorphism group of this group.
Keywords: finite group, almost simple group, prime graph. 
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     title = {Finite almost simple groups with prime graphs all of whose connected components are cliques},
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M. R. Zinov'eva; A. S. Kondrat'ev. Finite almost simple groups with prime graphs all of whose connected components are cliques. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 132-141. http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a14/