Magic Graphs - Softcover

Wallis, W. D.

Softcover

ISBN 10: 0817642528 ISBN 13: 9780817642525

Publisher: Springer, 2008

Synopsis

Magic squares, their origins lost in antiquity, are among the more popular mathematical recreations. "Magic" ideas have also been applied to graphs, labellings, and trees. Unlike many elusive subjects in this area, the problem for vertex-magic total labelings has been solved, and the details are examined in this volume.

About this title

Review

From the reviews: "The book is a beautiful collection of recent results on the topic of ‘magic labelings’." —MATHEMATICAL REVIEWS “The book should be accessible to advanced undergraduates or beginning graduate students. It might serve as inspiration for an REU program or as a source for senior undergraduate research projects, particularly if supervised by a mathematician who is truly ‘up’ on what is going on in this field.”(MAA REVIEWS)

Synopsis

This concise, self-contained book is unique in its focus on the theory of magic graphs/labeling and its applications to a number of new areas, e.g., networks, the construction of rulers, and pulse codes. It may serve as a graduate text for a special topics seminar in mathematics or computer science, or as a professional text for the researcher. Some key features: concise exposition from basic topics in graph theory to current research; theorems from graph theory and interesting counting arguments. 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 Sedlavc ek (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. In the last decade, there has been a resurgence of interest in "magic labelings" and other graph valuations, e.g., graceful labelings, due to a number of interesting results that have applications and are related to the problems of decomposing graphs into trees. 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 corresponding problem for vertex-magic total labelings has been solved, and the details are examined in this volume. The book also contains a number of recent constructions of magic graphs and verifications that families of graphs are magic.

Edition details

• Publisher: Springer
• Publication date: 2008
• Language: English
• ISBN 10: 0817642528
• ISBN 13: 9780817642525
• Binding: Paperback
• Number of pages: 168