Graph with given automorphism group and given chromatic index

Abstract

In 1938, Frucht [2] proved that every finite group may be represented by a graph, that is to say, given any finite group H, there is a graph G whose automorphism group is isomorphic to H. This paper pretends to prove that for every finite group H and for every positive integer number n â‰¥ 3, there exists a graph G, that represents H and whose chromatic index is n.