Graphs and Applications: An Introductory Approach

Graphs and Applications: An Introductory Approach

Mixed media product

By (author) Joan Aldous, By (author) Robin J. Wilson, Illustrated by S. Best

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  • Publisher: Springer London Ltd
  • Format: Mixed media product | 455 pages
  • Dimensions: 154mm x 230mm x 26mm | 581g
  • Publication date: 10 February 2003
  • Publication City/Country: England
  • ISBN 10: 185233259X
  • ISBN 13: 9781852332594
  • Edition: 3, Revised
  • Edition statement: 1st Corrected ed. 2000. Corr. 3rd printing 2003
  • Illustrations note: 192 black & white illustrations, biography
  • Sales rank: 465,824

Product description

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. Includes a large number of examples, problems and exercises.

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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!"

Table of contents

1 Introduction.- 1.1 Graphs, Digraphs and Networks.- 1.2 Classifying Problems.- 1.3 Seeking Solutions.- 2 Graphs.- 2.1 Graphs and Subgraphs.- 2.2 Vertex Degrees.- 2.3 Paths and Cycles.- 2.4 Regular and Bipartite Graphs.- 2.5 Case Studies.- Four Cubes Problem.- Social Networks.- Exercises 2.- 3 Eulerian and Hamiltonian Graphs.- 3.1 Exploring and Travelling.- 3.2 Eulerian Graphs.- 3.3 Hamiltonian Graphs.- 3.4 Case Studies.- Dominoes.- Diagram-Tracing Puzzles.- Knight's Tour Problem.- Gray Codes.- Exercises 3.- 4 Digraphs.- 4.1 Digraphs and Subdigraphs.- 4.2 Vertex Degrees.- 4.3 Paths and Cycles.- 4.4 Eulerian and Hamiltonian Digraphs.- 4.5 Case Studies.- Ecology.- Social Networks.- Rotating Drum Problem.- Ranking in Tournaments.- Exercises 4.- 5 Matrix Representations.- 5.1 Adjacency Matrices.- 5.2 Walks in Graphs and Digraphs.- 5.3 Incidence Matrices.- 5.4 Case Studies.- Interval Graphs.- Markov Chains.- Exercises 5.- 6 Tree Structures.- 6.1 Mathematical Properties of Trees.- 6.2 Spanning Trees.- 6.3 Rooted Trees.- 6.4 Case Study.- Braced Rectangular Frameworks.- Exercises 6.- 7 Counting Trees.- 7.1 Counting Labelled Trees.- 7.2 Counting Binary Trees.- 7.3 Counting Chemical Trees.- Exercises 7.- 8 Greedy Algorithms.- 8.1 Minimum Connector Problem.- 8.2 Travelling Salesman Problem.- Exercises 8.- 9 Path Algorithms.- 9.1 Fleury's Algorithm.- 9.2 Shortest Path Algorithm.- 9.3 Case Study.- Chinese Postman Problem.- Exercises 9.- 10 Paths and Connectivity.- 10.1 Connected Graphs and Digraphs.- 10.2 Menger's Theorem for Graphs.- 10.3 Some Analogues of Menger's Theorem.- 10.4 Case Study.- Reliable Telecommunication Networks.- Exercises 10.- 11 Planarity.- 11.1 Planar Graphs.- 11.2 Euler's Formula.- 11.3 Cycle Method for Planarity Testing.- 11.4 Kuratowski's Theorem.- 11.5 Duality.- 11.6 Convex Polyhedra.- Exercises 11.- 12 Vertex Colourings and Decompositions.- 12.1 Vertex Colourings.- 12.2 Algorithm for Vertex Colouring.- 12.3 Vertex Decompositions.- Exercises 12.- 13 Edge Colourings and Decompositions.- 13.1 Edge Colourings.- 13.2 Algorithm for Edge Colouring.- 13.3 Edge Decompositions.- Exercises 13.- 14 Conclusion.- 14.1 Classification of Problems.- 14.2 Efficiency of Algorithms.- 14.3 Another Classification of Problems.- Suggestions for Further Reading.- Appendix: Methods of Proof.- Computing Notes.- Solutions to Computer Activities.- Solutions to Problems in the Text.