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© 2019

Magic and Antimagic Graphs

Attributes, Observations and Challenges in Graph Labelings

Book
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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

  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

About the authors

Professor Martin Bača completed his PhD at Comenius University in 1992. He has written over 150 journal papers on graph labelings and metric dimension of graphs. He has supervised 10 PhD students and is an editorial board member of three scientific journals.

Emeritus Professor Mirka Miller completed her PhD from the University of New South Wales in 1990 under the supervision of Jenny Seberry. She has written over 200 academic articles and conference presentations, many on different aspects of graph labeling. Professor Miller launched the successful conference series IWOGL (International Workshop on Graph Labelings). She was part of various teams that introduced such graph labeling schemes as Vertex Antimagic Total Labeling (VATL), Edge Antimagic Total Labeling (EATL), Edge Irregular Total Labeling and Vertex Irregular Total Labeling. It is a testament to her work that articles are still being published under her name more than 3 years since she sadly passed away.

Dr Joe Ryan received his PhD from the University of Newcastle, Australia in 2004. Since then he has authored over 100 journal and refereed conference publications with almost half of these being in the field of graph labeling. Dr Ryan has been on the supervisory team of 11 successful PhD completions with 3 of those being related to graph labeling. He is a member of the IWOGL Steering Committee.

Associate Professor Andrea Semaničová-Feňovčíková received her PhD from Pavol Jozef Šafárik University in 2006. Her scientific interest covers graph labeling and metric dimension of graphs where she has published over 60 journal papers. Three PhD students are working under her supervision. She is a member of the editorial board of two scientific journals.

Bibliographic information

  • Book Title Magic and Antimagic Graphs
  • Book Subtitle Attributes, Observations and Challenges in Graph Labelings
  • Authors Martin Bača
    Mirka Miller
    Joe Ryan
    Andrea Semaničová-Feňovčíková
  • Series Title Developments in Mathematics
  • Series Abbreviated Title DEVM
  • 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 Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-030-24581-8
  • Softcover ISBN 978-3-030-24584-9
  • eBook ISBN 978-3-030-24582-5
  • Series ISSN 1389-2177
  • Series E-ISSN 2197-795X
  • Edition Number 1
  • Number of Pages XV, 322
  • Number of Illustrations 165 b/w illustrations, 0 illustrations in colour
  • Topics Graph Theory
    Combinatorics
    Discrete Mathematics in Computer Science
  • Buy this book on publisher's site

Reviews

“This book is especially relevant for senior undergraduate or postgraduate students with an interest in discrete mathematical structures or a major in graph labeling … . a valuable guide for postgraduate and early career researchers, as well as an excellent reference for graph theorists.” (Ioan Tomescu, zbMATH 1429.05001, 2020)