Magic Graphs

Magic labelings Magic squares are among the more popular mathematical recreations. Their origins are lost in antiquity; over the years, a number of generalizations have been proposed. In the early 1960s, Sedlacek asked whether "magic" ideas could be applied to graphs. Shortly afterward, Kotzig and Rosa formulated the study of graph label­ ings, or valuations as they were first called. A labeling is a mapping whose domain is some set of graph elements - the set of vertices, for example, or the se