Handicap distance antimagic graphs and incomplete tournaments

Abstract

Let G = (V, E) be a graph of order n. A bijection f: V → {1, 2,…, n} is called a distance magic labeling of G if there exists a positive integer μ such that for all v ϵ V, where N(v) is the open neighborhood of v. The constant μ is called the magic constant of the labeling f. Any graph which admits a distance magic labeling is called a distance magic graph. The bijection f: V → {1, 2,…, n} is called a d-distance antimagic labeling of G if for V = {v1, v2, …, vn} the sums form an arithmetic progression with difference d.We introduce a generalization of the well-known notion of magic rectangles called magic rectangle sets and use it to find a class of graphs with properties derived from the distance magic graphs. Then we use the graphs to construct a special kind of incomplete round robin tournaments, called handicap tournaments.