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Adventures in Graph Theory

  • Textbook
  • © 2017

Overview

Authors:
  1. W. David Joyner

    1. Department of Mathematics, United States Naval Academy, Annapolis, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Caroline Grant Melles

    1. Department of Mathematics, United States Naval Academy, Annapolis, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • Interdisciplinary textbook that does not assume a strong math background
  • Presents recent results in mathematics relevant to graph theory
  • Includes Sage code to explicitly illustrate computations
  • Includes supplementary material: sn.pub/extras

Part of the book series: Applied and Numerical Harmonic Analysis (ANHA)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-xxvi
    Download chapter PDF

  2. Introduction: Graphs—Basic Definitions

    • W. David Joyner, Caroline Grant Melles
    Pages 1-39

  3. Graphs and Laplacians

    • W. David Joyner, Caroline Grant Melles
    Pages 41-95

  4. Graphs as Manifolds

    • W. David Joyner, Caroline Grant Melles
    Pages 97-143

  5. Chip-Firing Games

    • W. David Joyner, Caroline Grant Melles
    Pages 145-208

  6. Interesting Graphs

    • W. David Joyner, Caroline Grant Melles
    Pages 209-243

  7. Cayley Graphs of Bent Functions and Codes

    • W. David Joyner, Caroline Grant Melles
    Pages 245-302

  8. Back Matter

    Pages 303-327
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Keywords

About this book

This textbook acts as a pathway to higher mathematics by seeking and illuminating the connections between graph theory and diverse fields of mathematics, such as calculus on manifolds, group theory, algebraic curves, Fourier analysis, cryptography and other areas of combinatorics. An overview of graph theory definitions and polynomial invariants for graphs prepares the reader for the subsequent dive into the applications of graph theory. To pique the reader’s interest in areas of possible exploration, recent results in mathematics appear throughout the book, accompanied with examples of related graphs, how they arise, and what their valuable uses are. The consequences of graph theory covered by the authors are complicated and far-reaching, so topics are always exhibited in a user-friendly manner with copious graphs, exercises, and Sage code for the computation of equations. Samples of the book’s source code can be found at github.com/springer-math/adventures-in-graph-theory.

The text is geared towards advanced undergraduate and graduate students and is particularly useful for those trying to decide what type of problem to tackle for their dissertation. This book can also serve as a reference for anyone interested in exploring how they can apply graph theory to other parts of mathematics.

Reviews

“The book illustrates and explores connections between graph theory and other areas of combinatorics. … This book is really interdisciplinary and it is a good source for mathematicians of diverse areas to understand its relations with graph theory. … The text is geared towards advanced undergraduate and graduate students and is particularly useful for those trying to decide what type of problem to tackle for their dissertation.” (Vilmar Trevisan, zbMATH 1406.05001, 2019)

Authors and Affiliations

  • Department of Mathematics, United States Naval Academy, Annapolis, USA

    W. David Joyner, Caroline Grant Melles

About the authors

David Joyner is a professor at the United States Naval Academy Mathematics Department. His research areas include error-correcting code, representation theory, and the applications of number theory to communication theory and cryptography.Caroline Grant Melles is a professor at the United States Naval Academy Mathematics Department.

Bibliographic Information

  • Book Title: Adventures in Graph Theory

  • Authors: W. David Joyner, Caroline Grant Melles

  • Series Title: Applied and Numerical Harmonic Analysis

  • DOI: https://doi.org/10.1007/978-3-319-68383-6

  • Publisher: Birkhäuser Cham

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer International Publishing AG 2017

  • Hardcover ISBN: 978-3-319-68381-2Published: 22 January 2018

  • Softcover ISBN: 978-3-319-88593-3Published: 06 June 2019

  • eBook ISBN: 978-3-319-68383-6Published: 28 December 2017

  • Series ISSN: 2296-5009

  • Series E-ISSN: 2296-5017

  • Edition Number: 1

  • Number of Pages: XXVI, 327

  • Number of Illustrations: 24 b/w illustrations, 56 illustrations in colour

  • Topics: Graph Theory, Fourier Analysis

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