Magic Graphs 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 index This 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. Preface List of Figures Preliminaries Edge Magic Total Labelings Vertex Magic Total Labelings Totally Magic Labelings Magic Type Labeling of Digraphs Notes on the Research Problems References Bibliography Answers to Selected Exercises Index.