Graph representations of finite Abelian groups
Bohdan Zelinka · Czechoslovak Mathematical Journal · 1981
To every graph G we can assign the group Aut G of all automorphisms of G. Making use of the results of A. Cay ley, R. Frucht [1] proved that for every finite group there exists a graph whose automorphism group is isomorphic to this group.Y. G. Vizing [2] suggested the investigation of special types of graphs assigned to groups which will be called here graph representations of groups.A graph representation of a group (5 is a graph with the property that its automorphism group is isomorphic to (5 and to any two vertices x, y of this graph there exists exactly one automorphism cp of this graph such that (p(x) -y.A graph representation of a group may be an undirected graph or a directed one.Therefore for a group (5 we shall distinguish its undirected graph representation l/i^(©) and its directed graph representation JDJR((5).