Wallis Magic Graphs

Erscheinungsjahr 2012
ISBN: 978-1-4612-0123-6
Verlag: Birkhäuser Boston
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 146 Seiten, Web PDF

Reihe: Mathematics and Statistics

This concise, self-contained book is unique in its focus on the theory of magic graphs/labeling and its applications to a number of new areas, e.g., networks, the construction of rulers, and pulse codes. It may serve as a graduate text for a special topics seminar in mathematics or computer science, or as a professional text for the researcher. Some key features: concise exposition from basic topics in graph theory to current research; theorems from graph theory and interesting counting arguments.

Zielgruppe

Graduate

Autoren/Hrsg.

Wallis, W.D.

Inhaltsverzeichnis

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 labeling.- 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.- References.- Answers to Selected Exercises.