Introduction to Graph Theory : H3 Mathematics
by Meng, Koh Khee; Fengming, Dong; Guan, Tay EngFormat: Hardcover
Pub. Date: 2007-06-30
Publisher(s): World Scientific Pub Co Inc
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Summary
Graph theory is an area in discrete mathematics which studies configurations involving a set of nodes interconnected by edges (called graphs). This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college. The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.
Table of Contents
| Preface | p. v |
| Notation | p. ix |
| Fundamental Concepts and Basic Results | p. 1 |
| The Konigsberg bridge problem | p. 1 |
| Multigraphs and graphs | p. 2 |
| p. 11 | |
| Vertex degrees | p. 14 |
| p. 23 | |
| Paths, cycles and connectedness | p. 26 |
| p. 34 | |
| Graph Isomorphisms, Subgraphs, the Complement of a Graph | p. 37 |
| Isomorphic graphs and isomorphisms | p. 37 |
| Testing isomorphic graphs | p. 41 |
| p. 47 | |
| Subgraphs of a graph | p. 49 |
| p. 57 | |
| The complement of a graph | p. 62 |
| p. 66 | |
| Bipartite Graphs and Trees | p. 69 |
| Bipartite graphs | p. 69 |
| p. 79 | |
| Trees | p. 82 |
| p. 87 | |
| (*) Spanning trees of a graph | p. 89 |
| p. 94 | |
| Vertex-colourings of Graphs | p. 95 |
| The four-colour problem | p. 95 |
| Vertex-colourings and chromatic number | p. 96 |
| p. 101 | |
| Enumeration of chromatic number | p. 102 |
| p. 107 | |
| Greedy colouring algorithm | p. 113 |
| p. 115 | |
| An upper bound for the chromatic number and Brooks' theorem | p. 119 |
| p. 121 | |
| Applications | p. 123 |
| p. 127 | |
| Matchings in Bipartite Graphs | p. 129 |
| Introduction | p. 129 |
| Matchings | p. 131 |
| p. 135 | |
| Hall's theorem | p. 139 |
| p. 143 | |
| System of distinct representatives | p. 147 |
| p. 152 | |
| Eulerian Multigraphs and Hamiltonian Graphs | p. 155 |
| Eulerian multigraphs | p. 155 |
| p. 158 | |
| Characterization of Eulerian multigraphs | p. 159 |
| p. 167 | |
| Around the world and Hamiltonian graphs | p. 171 |
| A necessary condition for a graph to be Hamiltonian | p. 177 |
| p. 180 | |
| Two sufficient conditions for a graph to be Hamiltonian | p. 184 |
| p. 188 | |
| Digraphs and Tournaments | p. 191 |
| Digraphs | p. 191 |
| p. 195 | |
| Basic concepts | p. 197 |
| p. 203 | |
| Tournaments | p. 209 |
| p. 213 | |
| Two properties of tournaments | p. 216 |
| p. 221 | |
| References | p. 223 |
| Books Recommended | p. 225 |
| Index | p. 227 |
| Table of Contents provided by Ingram. All Rights Reserved. |
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