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Ten Applications of Graph Theory

  • Book
  • © 1984

Overview

Authors:
  1. Hansjoachim Walther

    1. Institute of Technology, Ilmenau, GDR

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Part of the book series: Mathematics and its Applications (MAEE, volume 7)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-XII
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  2. Introduction

    • Hansjoachim Walther
    Pages 1-4
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  3. Flows and tensions on networks

    • Hansjoachim Walther
    Pages 5-68
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  4. The linear transportation problem

    • Hansjoachim Walther
    Pages 69-81
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  5. The cascade algorithm

    • Hansjoachim Walther
    Pages 82-99
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  6. Nonlinear transportation problems

    • Hansjoachim Walther
    Pages 100-125
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  7. Communication and supply networks

    • Hansjoachim Walther
    Pages 126-148
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  8. The assignment and the travelling salesman problems

    • Hansjoachim Walther
    Pages 149-171
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  9. Coding and decision graphs

    • Hansjoachim Walther
    Pages 172-186
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  10. Signal flow graphs

    • Hansjoachim Walther
    Pages 187-196
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  11. Minimum sets of feedback arcs

    • Hansjoachim Walther
    Pages 197-216
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  12. Embedding of planar graphs in the plane

    • Hansjoachim Walther
    Pages 217-244
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  13. Back Matter

    Pages 245-252
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Keywords

About this book

Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new bran­ ches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-tri­ vially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics. This program, Mathematics and Its Applications, is devoted to such (new) interrelations as exempla gratia: - a central concept which plays an important role in several different mathe­ matical and/or scientific specialized areas; - new applications of the results and ideas from one area of scientific endeavor into another; - influences which the results, problems and concepts of one field of enquiry have and have had on the development of another.

Reviews

`...contains an enormous amount of material for its size, and is a useful reference work for anyone interested in operations research.'
Bulletin of the London Mathematics Society, 18 (1986)

Authors and Affiliations

  • Institute of Technology, Ilmenau, GDR

    Hansjoachim Walther

Bibliographic Information

  • Book Title: Ten Applications of Graph Theory

  • Authors: Hansjoachim Walther

  • Series Title: Mathematics and its Applications

  • DOI: https://doi.org/10.1007/978-94-009-7154-7

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: VEB Deutscher Verlag der Wissenschaften, Berlin 1984

  • Hardcover ISBN: 978-90-277-1599-9Published: 31 January 1985

  • Softcover ISBN: 978-94-009-7156-1Published: 11 November 2011

  • eBook ISBN: 978-94-009-7154-7Published: 06 December 2012

  • Series ISSN: 0169-507X

  • Edition Number: 1

  • Number of Pages: 264

  • Additional Information: Originally published in German

  • Topics: Discrete Mathematics in Computer Science

  • Industry Sectors: IT & Software, Telecommunications

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