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Über dieses Buch

Magic and antimagic labelings are among the oldest labeling schemes in graph theory. This book takes readers on a journey through these labelings, from early beginnings with magic squares up to the latest results and beyond.

Starting from the very basics, the book offers a detailed account of all magic and antimagic type labelings of undirected graphs. Long-standing problems are surveyed and presented along with recent results in classical labelings. In addition, the book covers an assortment of variations on the labeling theme, all in one self-contained monograph.

Assuming only basic familiarity with graphs, this book, complete with carefully written proofs of most results, is an ideal introduction to graph labeling for students learning the subject. More than 150 open problems and conjectures make it an invaluable guide for postgraduate and early career researchers, as well as an excellent reference for established graph theorists.

Inhaltsverzeichnis

Frontmatter

Chapter 1. Introduction

Abstract
The area of graph theory has experienced fast development during the last 70 years, and among the huge diversity of concepts that appear while studying this subject, one that has gained a lot of popularity is the concept of labelings of graphs. In the intervening 50 years nearly 200 graph labeling techniques have been studied in over 2000 papers. A dynamic survey of graph labeling by Joseph Gallian provides useful information what has been done for any particular type of labeling.
Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková

Chapter 2. Magic and Supermagic Graphs

Abstract
This chapter introduces magic and supermagic graphs giving relevant definitions and tracing the evolution of magic graphs from its genesis in magic squares. The text proceeds to study magic and supermagic labelings on particular types of graphs and looks at the impact of various graph operations.
Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková

Chapter 3. Vertex-Magic Total Labelings

Abstract
This chapter is devoted to the study of vertex magic total labelings. Constructions are given for regular and non-regular graphs as well as for some standard graph families. These labelings are also explored for disjoint families of particular graphs.
Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková

Chapter 4. Edge-Magic Total Labelings

Abstract
After vertex magic total labelings, this chapter has a focus on edge magic total labelings. Labeling schemes are given for connected and disconnected graphs in addition to well-known graph families. Strong super edge magic labelings are introduced and relationships between super edge magic total labelings and other labeling schema are explored.
Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková

Chapter 5. Vertex-Antimagic Total Labelings

Abstract
Following the chapters on magic type labelings, this chapter begins the section of the book devoted to antimagic labelings. Vertex antimagic and super vertex antimagic labelings, both edge labels and total labels are investigated with labeling constrictions given for connected and disconnected graphs.
Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková

Chapter 6. Edge-Antimagic Total Labelings

Abstract
This chapter focuses on edge-antimagic graphs under both vertex labelings and total labelings. Super edge-antimagic total labelings are given for standard graphs and (a,1) edge-antimagic total labelings are introduced and explored.
Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková

Chapter 7. Graceful and Antimagic Labelings

Abstract
This chapter explores the relationship between antimagic labeling and alpha labelings and also the well-known graceful labelings. Much of this chapter looks at interesting labelings and structures on trees, including edge antimagic trees, alpha trees, and disjoint union of caterpillars.
Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková

Chapter 8. Conclusion

Abstract
The final chapter opens with a brief summary of the book. This is followed by a collection of conjectures and problems that, at the time of writing, were still unsolved. To the interested researcher this would undoubtedly be the most valuable chapter in the book.
Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková

Backmatter

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