Vertex Antimagic Total Labeling of Digraphs

In this paper we investigate the properties of (a, d)-vertex antimagic total labeling of a digraph D = (V, A).In this labeling, we assign to the vertices and arcs the consecutive integers from 1 to |V | + |A| and calculate the sum of labels at each vertex, i.e., the vertex label added to the labels on its out arcs.These sums form an arithmetical progression with initial term a and common difference d.We show the existence and nonexistence of (a, d)-vertex antimagic total labeling for several class of digraphs, and show how to construct labelings for generalized de Bruijn digraphs.We conclude this paper with an open problem suitable for further research.