Vertex in-magic arc labelings of digraphs

Let D=(V,A) be a directed graph with p vertices and q arcs. For v∈V, let I(v)={u∈V:(u,v)∈A}. A vertex in-magic arc labeling of D is a bijection f:A→{1,2,3,…,q} with the property that for every vertex v in V, ∑u∈I(v)f((u,v))=k for some constant k. A digraph D is called vertex in-magic if it admits a vertex in-magic arc labeling. In this paper we present several properties of vertex in-magic digraphs. We also characterize generalized de Bruijn digraphs which are vertex in-magic.