Matrices in Combinatorics and Graph Theory

  • Bolian Liu
  • Hong-Jian Lai

Part of the Network Theory and Applications book series (NETA, volume 3)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Bolian Liu, Hong-Jian Lai
    Pages 1-46
  3. Bolian Liu, Hong-Jian Lai
    Pages 47-96
  4. Bolian Liu, Hong-Jian Lai
    Pages 97-159
  5. Bolian Liu, Hong-Jian Lai
    Pages 161-216
  6. Bolian Liu, Hong-Jian Lai
    Pages 217-274
  7. Bolian Liu, Hong-Jian Lai
    Pages 275-281
  8. Back Matter
    Pages 283-310

About this book

Introduction

Combinatorics and Matrix Theory have a symbiotic, or mutually beneficial, relationship. This relationship is discussed in my paper The symbiotic relationship of combinatorics and matrix theoryl where I attempted to justify this description. One could say that a more detailed justification was given in my book with H. J. Ryser entitled Combinatorial Matrix Theon? where an attempt was made to give a broad picture of the use of combinatorial ideas in matrix theory and the use of matrix theory in proving theorems which, at least on the surface, are combinatorial in nature. In the book by Liu and Lai, this picture is enlarged and expanded to include recent developments and contributions of Chinese mathematicians, many of which have not been readily available to those of us who are unfamiliar with Chinese journals. Necessarily, there is some overlap with the book Combinatorial Matrix Theory. Some of the additional topics include: spectra of graphs, eulerian graph problems, Shannon capacity, generalized inverses of Boolean matrices, matrix rearrangements, and matrix completions. A topic to which many Chinese mathematicians have made substantial contributions is the combinatorial analysis of powers of nonnegative matrices, and a large chapter is devoted to this topic. This book should be a valuable resource for mathematicians working in the area of combinatorial matrix theory. Richard A. Brualdi University of Wisconsin - Madison 1 Linear Alg. Applies., vols. 162-4, 1992, 65-105 2Camhridge University Press, 1991.

Keywords

Matrix Matrix Theory algebra calculus combinatorics graph theory linear algebra

Authors and affiliations

  • Bolian Liu
    • 1
  • Hong-Jian Lai
    • 2
  1. 1.Department of MathematicsSouth China Normal UniversityGuangzhouP.R. China
  2. 2.Department of MathematicsWest Virginia UniversityMorgantownUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3165-1
  • Copyright Information Springer-Verlag US 2000
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-4834-2
  • Online ISBN 978-1-4757-3165-1
  • Series Print ISSN 1568-1696
  • About this book