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Line Graphs and Line Digraphs

  • Book
  • © 2021

Overview

Authors:
  1. Lowell W. Beineke

    1. Department of Mathematical Sciences, Purdue University Fort Wayne, Fort Wayne, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Jay S. Bagga

    1. Department of Computer Science, Ball State University, Muncie, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  • The first monograph devoted exclusively to Line Graphs and Line Digraphs
  • Provides a comprehensive, historical and up-to-date reference on the subject
  • Covers line graphs and line digraphs from their origins to current research

Part of the book series: Developments in Mathematics (DEVM, volume 68)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xviii
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  2. Line Graphs

    1. Front Matter

      Pages 1-1
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    2. Fundamentals of Line Graphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 3-15

    3. Line Graph Isomorphisms

      • Lowell W. Beineke, Jay S. Bagga
      Pages 17-23

    4. Characterizations of Line Graphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 25-49

    5. Spectral Properties of Line Graphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 51-59

    6. Planarity of Line Graphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 61-86

    7. Connectivity of Line Graphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 87-95

    8. Traversability in Line Graphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 97-108

    9. Colorability in Line Graphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 109-125

    10. Distance and Transitivity in Line Graphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 127-141

  3. Line Digraphs

    1. Front Matter

      Pages 143-143
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    2. Fundamentals of Line Digraphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 145-158

    3. Characterizations of Line Digraphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 159-171

    4. Iterated Line Digraphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 173-199

  4. Generalizations

    1. Front Matter

      Pages 201-201
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    2. Total Graphs and Total Digraphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 203-217

    3. Path Graphs and Path Digraphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 219-232

    4. Super Line Graphs and Super Line Digraphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 233-256

    5. Line Graphs of Signed Graphs

      • Lowell W. Beineke, Jay S. Bagga
      Pages 257-267
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Keywords

About this book

In the present era dominated by computers, graph theory has come into its own as an area of mathematics, prominent for both its theory and its applications. One of the richest and most studied types of graph structures is that of the line graph, where the focus is more on the edges of a graph than on the vertices.

A subject worthy of exploration in itself, line graphs are closely connected to other areas of mathematics and computer science. This book is unique in its extensive coverage of many areas of graph theory applicable to line graphs. The book has three parts. Part I covers line graphs and their properties, while Part II looks at features that apply specifically to directed graphs, and Part III presents generalizations and variations of both line graphs and line digraphs.

Line Graphs and Line Digraphs is the first comprehensive monograph on the topic. With minimal prerequisites, the book is accessible to most mathematicians and computer scientistswho have had an introduction graph theory, and will be a valuable reference for researchers working in graph theory and related fields.

Authors and Affiliations

  • Department of Mathematical Sciences, Purdue University Fort Wayne, Fort Wayne, USA

    Lowell W. Beineke

  • Department of Computer Science, Ball State University, Muncie, USA

    Jay S. Bagga

About the authors

Lowell Beineke is the Schrey Professor Emeritus of Mathematics at Purdue University, having retired in 2020 after more than a half-century at Purdue University Fort Wayne, Indiana. He received his baccalaureate degree from Purdue University and his doctorate from the University of Michigan. His mathematical research has been in the field of graph theory, in which he has been author of more than a hundred papers and a co-editor of ten books on topics in graph theory. He also served for five years as Editor of The College Mathematics Journal. His interests in graph theory are broad. In addition to line graphs and line digraphs, they include the thickness of graphs, crossing numbers, tournaments, graph decompositions, graph labeling, and multi-dimensional trees. His various honors include being entered into Purdue University’s Book of Great Teachers, the Beineke award established at Purdue University Fort Wayne, being a recipient of the Meritorious Service award from the Mathematical Association of America, having a special issue of the AKCE International Journal of Graph and Combinatorics devoted to his work, and being listed in Who’s Who in America.

Jay Bagga has been a Professor of Computer Science at Ball State University since 1992. He received his baccalaureate degree from University of Mumbai and his doctorate from Purdue University. His areas of research interest include graph theory, graph algorithms and their applications to computer science. He has co-edited special issues of graph theory journals and proceedings, and has published over sixty papers in line graphs and line digraphs, tournaments, graceful labelling and algorithms, Hamiltonian graphs, vulnerability parameters of graphs, and applications to bioinformatics and other related areas in computer science. His research has been funded by, among others, the U. S. Office of Naval Research, and the U. S. Department of State. His various honors include aSenior Fulbright Award, U. S. Vietnam Educational Foundation Faculty Scholar Award, Midwest Graph Theory Conference Harary Plenary Lecture Speaker, and Ball State University Outstanding Faculty and Researcher of the Year Awards.

Bibliographic Information

  • Book Title: Line Graphs and Line Digraphs

  • Authors: Lowell W. Beineke, Jay S. Bagga

  • Series Title: Developments in Mathematics

  • DOI: https://doi.org/10.1007/978-3-030-81386-4

  • Publisher: Springer Cham

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

  • Copyright Information: Springer Nature Switzerland AG 2021

  • Hardcover ISBN: 978-3-030-81384-0Published: 30 October 2021

  • eBook ISBN: 978-3-030-81386-4Published: 29 October 2021

  • Series ISSN: 1389-2177

  • Series E-ISSN: 2197-795X

  • Edition Number: 1

  • Number of Pages: XVIII, 300

  • Number of Illustrations: 142 b/w illustrations, 58 illustrations in colour

  • Topics: Graph Theory, Discrete Mathematics in Computer Science

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