Resumen de Graph with given automorphic group and given nuclear number

Eduardo Montenegro

• In 1938, Frucht proved that every finite group may be represented by a graph; in other words, given any finite group H, there is graph G whose automorphism group is isomorphic to H. Starting from this result a great many mathematicians have studied the following problem: "Given a finite group H and given a property P, is there a graph G that represents H and that satisfies the property P ?" The aim of this paper is to solve a problem of such characteristics. The statement we get is the following: "Every finite group H may be represented by a graph G whose nuclear number is n ≥ 2 , where n is a given positive integer "