magic squares are among the more popular mathematical recreations. over the last 50 years, many generalizations of “magic” ideas have been applied to graphs. recently there has been a resurgence of interest in “magic labelings” due to a number of results that have applications to the problem of decomposing graphs into trees. key features of this second edition include:· a new chapter on magic labeling of directed graphs· applications of theorems from graph theory and interesting counting arguments· new research problems and exercises covering a range of difficulties· a fully updated bibliography and indexthis concise, self-contained exposition is unique in its focus on the theory of magic graphs/labelings. it may serve as a graduate or advanced undergraduate text for courses in mathematics or computer science, and as reference for the researcher.