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Magic and Antimagic Graphs

Attributes, Observations and Challenges in Graph Labelings

  • Martin Bača
  • Mirka Miller
  • Joe Ryan
  • Andrea Semaničová-Feňovčíková

Part of the Developments in Mathematics book series (DEVM, volume 60)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková
    Pages 1-3
  3. Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková
    Pages 5-88
  4. Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková
    Pages 89-116
  5. Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková
    Pages 117-157
  6. Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková
    Pages 159-203
  7. Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková
    Pages 205-271
  8. Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková
    Pages 273-297
  9. Martin Bača, Mirka Miller, Joe Ryan, Andrea Semaničová-Feňovčíková
    Pages 299-303
  10. Back Matter
    Pages 305-322

About this book

Introduction

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.

Keywords

Graph labelings Magic graphs Super magic graphs Antimagic graphs Super antimagic graphs Total labelings Vertex magic total labelings Edge magic total labelings Vertex antimagic total labelings Edge antimagic total labelings

Authors and affiliations

  • Martin Bača
    • 1
  • Mirka Miller
    • 2
  • Joe Ryan
    • 3
  • Andrea Semaničová-Feňovčíková
    • 4
  1. 1.Department of Applied Mathematics and InformaticsTechnical UniversityKošiceSlovakia
  2. 2.School of Mathematical and Physical Sciences, University of Newcastle, Australia, Department of MathematicsUniversity of West BohemiaPilsenCzech Republic
  3. 3.School of Electrical Engineering and ComputingUniversity of NewcastleAustralia
  4. 4.Department of Applied Mathematics and InformaticsTechnical UniversityKošiceSlovakia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-24582-5
  • Copyright Information Springer Nature Switzerland AG 2019
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-030-24581-8
  • Online ISBN 978-3-030-24582-5
  • Series Print ISSN 1389-2177
  • Series Online ISSN 2197-795X
  • Buy this book on publisher's site