The exponent of the primitive Cayley digraphs on finite abelian groups
Let \(S\) be the set of the central elements of a finite group \(G\). The authors find necessary and sufficient conditions for a Cayley digraph to be primitive. They also show that the exponent of a primitive Cayley digraph on an abelian group is \(n-1\), \([n/2]\), \([n/2] -1\), or does not exceed \([n/3] +1\). A characterization of digraphs corresponding to the first three exponents is given.
scientific article; zbMATH DE number 1133169