Magic graphs.

*(English)*Zbl 0979.05001
Boston, MA: Birkhäuser. xiv, 146 p. (2001).

As the author points out in the preface, there are three main reasons for a monograph studying magic labellings of graphs: (1) magic labellings provide an introduction to the more general topic of graph labellings, (2) a focused book, on one particular problem, is a good guide for graduate students beginning research so they can see how new mathematics comes into existence, and (3) in recent years a number of researchers have found the topic of magic labellings of graphs fascinating, but they have not communicated very well with each other, and so hopefully this volume will obviate unnecessary repetitions of intellectual effort and help unifying notation, which is currently diverse and self-contradictory.

The introductory chapter covers briefly the basics of graph theory and introduces various kinds of magic labellings of graphs. The main three chapters that follow are devoted to the three main types of magic labellings: edge-magic, vertex-magic, and totally magic labellings, respectively. Exercises and research problems occur throughout. The bibliography comprises 59 items. Not many mathematical prerequisites are needed to read this book although the reader should have some mathematical maturity.

The introductory chapter covers briefly the basics of graph theory and introduces various kinds of magic labellings of graphs. The main three chapters that follow are devoted to the three main types of magic labellings: edge-magic, vertex-magic, and totally magic labellings, respectively. Exercises and research problems occur throughout. The bibliography comprises 59 items. Not many mathematical prerequisites are needed to read this book although the reader should have some mathematical maturity.

Reviewer: A.Rosa (Hamilton/Ontario)

##### MSC:

05-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to combinatorics |

05C78 | Graph labelling (graceful graphs, bandwidth, etc.) |

68R10 | Graph theory (including graph drawing) in computer science |

90B18 | Communication networks in operations research |

90C35 | Programming involving graphs or networks |