Degree sets for digraphs

Abstract

The degree setD _D of a digraphD is the set of outdegrees of the vertices ofD. For a finite, nonempty setS of nonnegative integers, it is shown that there exists an asymmetric digraph (oriented graph)D such thatD _D =S. Furthermore, the minimum order of such a digraphD is determined. Also, given two finite sequences of nonnegative integers, a necessary and sufficient condition is provided for which these sequences are the outdegree sequences of the two sets of an asymmetric bipartite digraph.