Some applications of the subtitution in graph

Abstract

In 1949 R. Frucht established that any finite group can be represented by a graph of degree three in the sense that automorphism group of the graph is isomorphic to the given group. In 1957 G. Sabidussi gave another step in this direction, proving that every finite group can be represented by an infinite number of regular graphs. The main result of this work is to give a proof of the Sabidussi’s theorem by operation of the graph called substitution, that consists of replacing any vertex by a graph.