Graphs and Applications

An Introductory Approach

By: Joan M. Aldous, S. Best (Illustrator), Robin J. Wilson

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Paperback | 22 March 2000 | Edition Number 3

At a Glance

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460 Pages

Edition Type
Revised

Dimensions(cm)
22.86 x 16.51 x 2.54

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Discrete Mathematics is one of the fastest growing areas in mathematics today with an ever-increasing number of courses in schools and universities. Graphs and Applications is based on a highly successful Open University course and the authors have paid particular attention to the presentation, clarity and arrangement of the material, making it ideally suited for independent study and classroom use. An important part of learning graph theory is problem solving; for this reason large numbers of examples, problems (with full solutions) and exercises (without solutions) are included.Accompanying the book is a CD-ROM comprising a Graphs Database, containing all the simple unlabelled graphs with up to seven vertices, and a Graphs Editor that enables students to construct and manipulate graphs. Both the Database and Editor are simple to use and allow students to investigate graphs with ease. Computing Notes and suggested activities are provided.

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From the reviews: BULLETIN OF MATHEMATICS BOOKS "? very nice (as you might expect from Wilson) but very low level graph theory text?t even has a CD!"

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Introduction	p. 1
Graphs, Digraphs and Networks	p. 1
Classifying Problems	p. 20
Seeking Solutions	p. 23
Graphs	p. 25
Graphs and Subgraphs	p. 25
Vertex Degrees	p. 35
Paths and Cycles	p. 38
Regular and Bipartite Graphs	p. 43
Eulerian and Hamiltonian Graphs	p. 61
Exploring and Travelling	p. 61
Eulerian Graphs	p. 64
Hamiltonian Graphs	p. 71
Digraphs	p. 84
Digraphs and Subdigraphs	p. 84
Vertex Degrees	p. 92
Paths and Cycles	p. 94
Eulerian and Hamiltonian Digraphs	p. 97
Matrix Representations	p. 112
Adjacency Matrices	p. 113
Walks in Graphs and Digraphs	p. 117
Incidence Matrices	p. 122
Tree Structures	p. 138
Mathematical Properties of Trees	p. 140
Spanning Trees	p. 144
Rooted Trees	p. 146
Counting Trees	p. 163
Counting Labelled Trees	p. 164
Counting Binary Trees	p. 171
Counting Chemical Trees	p. 174
Greedy Algorithms	p. 182
Minimum Connector Problem	p. 182
Travelling Salesman Problem	p. 191
Path Algorithms	p. 202
Fleury's Algorithm	p. 202
Shortest Path Algorithm	p. 204
Paths and Connectivity	p. 216
Connected Graphs and Digraphs	p. 216
Menger's Theorem for Graphs	p. 226
Some Analogues of Menger's Theorem	p. 230
Planarity	p. 242
Planar Graphs	p. 243
Euler's Formula	p. 247
Cycle Method for Planarity Testing	p. 256
Kuratowski's Theorem	p. 260
Duality	p. 264
Convex Polyhedra	p. 268
Vertex Colourings and Decompositions	p. 277
Vertex Colourings	p. 277
Algorithm for Vertex Colouring	p. 288
Vertex Decompositions	p. 292
Edge Colourings and Decompositions	p. 303
Edge Colourings	p. 303
Algorithm for Edge Colouring	p. 313
Edge Decompositions	p. 317
Conclusion	p. 332
Classification of Problems	p. 332
Efficiency of Algorithms	p. 338
Another Classification of Problems	p. 339
Suggestions for Further Reading	p. 346
Methods of Proof	p. 348
Computing Notes	p. 354
Solutions to Computer Activities	p. 380
Solutions to Problems in the Text	p. 384
Index	p. 439
Table of Contents provided by Blackwell. All Rights Reserved.

Graphs and Applications

An Introductory Approach

At a Glance

Paperback

Industry Reviews

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