Graph with given automorphic group and given nuclear number
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 "
[ 2] Frucht, R.: Herstellung von Graphen mit vorgegebener abstrakter Gruppe, Compositio Math., 6, 239-250, 1938.
[ 3] Montenegro, E.: Un resultado sobre el orden y el tamaño de grafos que representan a un grupo finito, Visiones Científicas, 2, 49-71, 1986, Valparaíso, Chile.
[ 4] Sabidussi, G.: Graphs with given group and given graph-theoretical properties, Canad. J. Math., 9, 515-525, 1957.
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