Parameswari, R.; Rajeswari, R. Edge graceful labeling of Paley digraph. (English) Zbl 1452.05163 J. Comb. Math. Comb. Comput. 112, 33-42 (2020). Summary: 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 W. Ananchuen and L. Caccetta [Discrete Math. 306, No. 22, 2954–2961 (2006; Zbl 1107.05078)]. R. L. Graham and J. H. Spencer [Can. Math. Bull. 14, 45–48 (1971; Zbl 0209.55804)] defined tournament with \(q\) vertices where \(q\equiv 3 \pmod 4\) 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. MSC: 05C78 Graph labelling (graceful graphs, bandwidth, etc.) 05C20 Directed graphs (digraphs), tournaments 05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.) Keywords:Paley digraph; odd edge graceful labeling; super edge graceful labeling; strong edge graceful labeling Citations:Zbl 1107.05078; Zbl 0209.55804 PDFBibTeX XMLCite \textit{R. Parameswari} and \textit{R. Rajeswari}, J. Comb. Math. Comb. Comput. 112, 33--42 (2020; Zbl 1452.05163)