Graph Labelings and Tournament Scheduling

Abstract

During my research I studied and became familiar with distance magic and distance antimagic labelings and their relation to tournament scheduling. Roughly speaking, the relation is as follows. Let the vertices on the graph represent teams in a tournament, and let an edge between two vertices a and b represent that team a will play team b in the tournament. Further, suppose we can rank the teams based on previous games, say, the preceding season. These integer rankings become labels for the vertices. Of particular interest were handicap tournaments, that is, tournaments designed to give each team a more balanced chance of winning.