Edge Graceful Labeling of Paley Digraph

A digraph G is finite and is denoted as \(G(V,E)\) with \(V\) as set of nodes and E as set of directed arcs which is exact. If \((u, v)\) is an arc in a digraph \(D\), we say vertex u dominates vertex v. A special digraph arises in round robin tournaments. Tournaments with a special quality \(Q(n, k)\) have been studied by Ananchuen and Caccetta. Graham and Spencer defined tournament with \(q\) vertices
where \(q \equiv 3 (mod 4)\) is a prime. It was named suitably as Paley digraphs in respect deceased Raymond Paley, he was the person used quadratic residues to construct Hadamard matrices more than 50 years earlier. This article is based on a special class of graph called Paley digraph which admits odd edge graceful, super edge graceful and strong edge graceful labeling.