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Author Baca, Martin, 1956-
Title Magic and Antimagic Graphs : Attributes, Observations and Challenges in Graph Labelings / Martin Baca, Mirka Miller, Joe Ryan, Andrea Semanicova-Fenovcikova.
Imprint Cham : Springer, 2019.

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Author Baca, Martin, 1956-
Series Developments in Mathematics Ser. ; v.60.
Developments in mathematics ; v. 60.
Subject Graph labelings.
Alt Name Miller, Mirka, 1949-
Ryan, Joe (Computer scientist)
Semanicova-Fenovcikova, Andrea.
Description 1 online resource (330 pages).
Note Description based upon print version of record.
5.6 Super Vertex-Antimagic Total Labeling of Disconnected Graphs
Contents Intro; Preface; Contents; List of Figures; 1 Introduction; 2 Magic and Supermagic Graphs; 2.1 Definition of Magic and Supermagic Labeling; 2.2 Magic Squares; 2.3 Characterization of Magic Graphs; 2.4 Generalization of Magic Labeling; 2.5 Conditions for a Graph to be Supermagic; 2.6 Number of Edges in Magic and Supermagic Graphs; 2.6.1 Magic Graphs; 2.6.2 Supermagic Graphs; 2.7 Magic and Supermagic Line Graphs; 2.7.1 Magic Line Graphs; 2.7.2 Supermagic Line Graphs; 2.8 Regular Magic and Supermagic Graphs; 2.8.1 Complete Graphs and Complete Multipartite Graphs; 2.8.2 Cartesian Product of Graphs
2.8.3 Lexicographic Product (Composition) of Graphs2.8.4 Zykovian Product of Graphs; 2.8.5 Circulant Graphs; 2.8.6 Constructions Using Vertex-Antimagic Graphs; 2.8.7 Constructions Using Double-Consecutive Labeling; 2.8.8 Constructions Using Degree-Magic Labeling; 2.9 Non-regular Magic and Supermagic Graphs; 2.9.1 Insertion of a New Edge; 2.9.2 Deletion of an Edge; 2.9.3 Contraction of an Edge; 2.9.4 Splitting a Vertex and Adding an Edge; 2.9.5 Disjoint Union of Regular Graphs; 2.9.6 Constructions Using (a,1)-Vertex-Antimagic Edge Graphs; 2.9.7 Join of Graphs
2.9.8 Other Magic and Supermagic Non-regular Graphs2.10 Related Topics; 3 Vertex-Magic Total Labelings; 3.1 Vertex-Magic Total Labelings of Regular Graphs; 3.1.1 Cycles; 3.1.2 Complete Graphs; 3.1.3 Generalized Petersen Graphs; 3.1.4 Two Families of Convex Polytopes; 3.1.5 Cartesian Product of Graphs; 3.1.6 Knodel Graphs; 3.1.7 General Results for Regular Graphs; 3.2 The Existence of Vertex-Magic Total Labelings; 3.3 Vertex-Magic Total Labelings of Non-regular Graphs; 3.3.1 Complete Bipartite Graphs; 3.3.2 Complete Multipartite Graphs; 3.3.3 Wheels and Related Graphs
3.4 Disjoint Unions of Graphs4 Edge-Magic Total Labelings; 4.1 Basic Ideas; 4.2 Edge-Magic Total and Super Edge-Magic Total Labelings of Regular Graphs; 4.2.1 Cycles; 4.2.2 Complete Graphs; 4.2.3 Generalized Petersen Graphs; 4.3 Labelings of Certain Families of Connected Graphs; 4.3.1 Wheels; 4.3.2 Fans and Friendship Graphs; 4.3.3 Ladders and Generalized Prisms; 4.3.4 Paths; 4.3.5 Path-Like Trees; 4.4 Labelings of Certain Families of Disconnected Graphs; 4.4.1 Disjoint Union of Stars; 4.4.2 Disjoint Union of Paths; 4.4.3 Disjoint Union of Path-Like Trees; 4.5 Strong Super Edge-Magic Labeling
4.6 Relationships Super Edge-Magic Total Labelings with Other Labelings5 Vertex-Antimagic Total Labelings; 5.1 Vertex-Antimagic Edge Labeling; 5.2 Vertex-Antimagic Total and Super Vertex-Antimagic Total Labelings; 5.3 Relationship Between Vertex-Antimagic Edge and (Super) Vertex-Antimagic Total Labelings; 5.4 Vertex-Antimagic Total Labelings of Cycles and Paths; 5.5 Super Vertex-Antimagic Total Labelings of Certain Families of Connected Graphs; 5.5.1 Cycles and Paths; 5.5.2 Generalized Petersen Graphs; 5.5.3 Trees and Unicyclic Graphs
Summary 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.
ISBN 9783030245825 (electronic bk.)
3030245829 (electronic bk.)
ISBN/ISSN 10.1007/978-3-030-24
OCLC # 1120697050
Additional Format Print version: Baca, Martin Magic and Antimagic Graphs : Attributes, Observations and Challenges in Graph Labelings Cham : Springer,c2019 9783030245818.

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