Some Results on the Degree of Vertices of the Power Digraph and Its Complement

This work is based on the ideas of L. Somer and M. Krizek, On a connection of Number theory with Graph theory. In this work, we introduce the concept of Universal directed graph Un and we also define the complement of the digraph Γ(n,2). We study some relations between the digraph Γ(n,2) and its complement digraph Γ(n,2) in terms of degree of a vertex and directed arcs. A result for the number of fixed points in the digraph Γ(n,2) is established. We also established some results on the degree of a vertex w. r. t. a subset of the vertex set of the digraphs Γ(n,2) and Γ(n,2).