Magic Graphs / Edition 1

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2001 Paperback Good Item may show signs of shelf wear. Pages may include limited notes and highlighting. Includes supplemental or companion materials if applicable. Access ... codes may or may not work. Connecting readers since 1972. Customer service is our top priority. Read more Show Less

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Magic squares, their origins lost in antiquity, are among the more popular mathematical recreations. "Magic" ideas have also been applied to graphs, labellings, and trees. Unlike many elusive subjects in this area, the problem for vertex-magic total labelings has been solved, and the details are examined in this volume.

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Product Details

  • ISBN-13: 9780817642525
  • Publisher: Springer-Verlag New York, LLC
  • Publication date: 6/15/2001
  • Edition description: New Edition
  • Edition number: 1
  • Pages: 160
  • Product dimensions: 9.21 (w) x 6.14 (h) x 0.36 (d)

Table of Contents

• List of Figures
• 1. Preliminaries
• 1.1 Magic
• 1.2 Graphs
• 1.3 Labelings
• 1.4 Magic Labeling
• 1.5 Some Applications of Magic Labelings
• 2. Edge-Magic Total Labelings
• 2.1 Basic Ideas
• 2.2 Graphs with No Edge-Magic Total Labelings
• 2.3 Cliques and Complete Graphs
• 2.4 Cycles
• 2.5 Complete Bipartite Graphs
• 2.6 Wheels
• 2.7 Trees
• 2.8 Disconnected Graphs
• 2.9 Strong Edge-Magic Total Labelings
• 2.10 Edge-Magic Injections
• 3. Vertex-Magic Total Labelings
• 3.1 Basic Ideas
• 3.2 Regular Graphs
• 3.3 Cycles and Paths
• 3.4 Vertex-Magic Total Labelings of Wheels
• 3.5 Vertex-Magic Total Labelings of Complete Bipartite Graphs
• 3.6 Graphs with Vertices of Degree One
• 3.7 The Complete Graphs
• 3.8 Disconnected Graphs
• 3.9 Vertex-Magic Injections
• 4. Totally Magic Labelings
• 4.1 Basic Ideas
• 4.2 Isolates and Stars
• 4.3 Forbidden Configurations
• 4.4 Unions of Triangles
• 4.5 Small Graphs
• 4.6 Totally Magic Injections
• Notes on the Research Problems
• Bibliography
• Solutions to Selected Exercises
• Index

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