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. 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. Preliminaries -- Edge-magic Total Labelings -- Vertex-magic Total Labelings -- Totally Magic Labelings -- Magic Type Labelings Of Digraphs. Alison M. Marr, W.d. Wallis. Includes Bibliographical References (p. 163-169) And Index. 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 -- Source other than Library of Congress This concise, self-contained exposition is unique in its focus on the theory of magic graphs/labelings and its application to a number of new areas. It may serve as a graduate text for courses and seminars in mathematics or computer science, or as a professional text for the researcher. Front Matter....Pages i-xvi Preliminaries....Pages 1-14 Edge-Magic Total Labelings....Pages 15-69 Vertex-Magic Total Labelings....Pages 71-109 Totally Magic Labelings....Pages 111-134 Magic Type Labelings of Digraphs....Pages 135-157 Back Matter....Pages 159-186 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.