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    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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    DescriptionDiscrete 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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  • Full bibliographic data for Graphs and Applications

    Graphs and Applications
    An Introductory Approach
    Authors and contributors
    By (author) Joan Aldous, By (author) Robin J. Wilson, Illustrated by S. Best
    Physical properties
    Format: Mixed media product
    Number of pages: 455
    Width: 154 mm
    Height: 230 mm
    Thickness: 26 mm
    Weight: 581 g
    ISBN 13: 9781852332594
    ISBN 10: 185233259X

    BIC E4L: MAT
    B&T Book Type: NF
    Nielsen BookScan Product Class 3: S7.9T
    LC subject heading:
    B&T Merchandise Category: TXT
    B&T Modifier: Region of Publication: 03
    B&T Modifier: Academic Level: 01
    B&T General Subject: 710
    Ingram Subject Code: MA
    B&T Modifier: Text Format: 06
    Warengruppen-Systematik des deutschen Buchhandels: 16280
    BIC subject category V2: PBV
    DC22: 511.5
    DC21: 511.5
    BISAC V2.8: MAT008000
    B&T Approval Code: A51443500
    BISAC V2.8: MAT013000, MAT036000
    DC22: 511/.5
    LC subject heading:
    Libri: KOMB6000
    LC subject heading:
    LC classification: QA166 .A425 2000, QA1-939, QA164-167.2
    Thema V1.0: PBV
    3, Revised
    Edition statement
    1st Corrected ed. 2000. Corr. 3rd printing 2003
    Illustrations note
    192 black & white illustrations, biography
    Springer London Ltd
    Imprint name
    Springer London Ltd
    Publication date
    10 February 2003
    Publication City/Country
    Review quote
    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.