E-Super Vertex In-Magic Total 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 total labeling of D is a bijection f from V∪A→{1,2,3,…,p+q} with the property that for every v∈V, f(v)+∑u∈I(v)f((u,v))=k for some constant k. Such a labeling is called an E-super vertex in-magic total labeling (E-SVIMT labeling) if f(A)={1,2,3,…,q}. A digraph D is called an E-super vertex in magic total digraph (E-SVIMT digraph) if D admits an E-SVIMT labeling. In this paper we present several properties of E-SVIMT digraphs. We also characterize generalized de Bruijn digraphs which admit E-SVIMT labelings.