Magic Graphs

"Magic squares, their origins lost in antiquity, are among the more popular mathematical recreations. Over the years a number of generalizations have been proposed, going back in the last century to Sedlacek (early 1960s) who asked whether "magic" ideas could be applied to graphs. Around the same time Kotzig and Rosa formulated the study of graph labelings, or valuations as they were first called.". "Trees remain an elusive subject. From the pure mathematics viewpoint, no progress has been made in answering the question: Does every tree have an edge-magic total labeling? However, the…