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We continue the study of prime graphs of finite groups, also known asGruenberg-Kegel graphs. The vertices of the prime graph of a finite group arethe prime divisors of the group order, and two vertices $p$ and $q$ areconnected by an edge if and only if there is an element of order $pq$ in thegroup. Prime graphs of solvable groups have been characterized in graphtheoretical terms only, as have been the prime graphs of groups whose onlynonsolvable composition factor is $A_5$. In this paper we classify the primegraphs of all groups whose composition factors have arithmetically smallorders, that is, have no more than three prime divisors in their orders. Wefind that all such graphs have $3$-colorable complements, and we provide fullcharacterizations of the prime graphs of such groups based on the exact typeand multiplicity of the nonabelian composition factors of the group.

The Prime Graphs of Groups With Arithmetically Small Composition Factors