Vosperian and superconnected Abelian Cayley digraphs

A digraphX is said to be Vosperian if any fragment has cardinality either 1 or|V(X)| – d ⁺ (X) – 1.A digraph is said to be superconnected if every minimum cutset is the set of vertices adjacent from or to some vertex.In this paper we characterize Vosperian and superconnected Abelian Cayley directed graphs. Our main tool is a difficult theorem of J.H. Kemperman from Additive Group Theory.In particular we characterize Vosperian and superconnected loops network (also called circulants).