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Network Theory and Applications

Matrices in Combinatorics and Graph Theory

Authors: Bolian Liu, Hong-Jian Lai

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Hardcover $189.00
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About this book

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.

Table of contents (6 chapters)

  • Matrices and Graphs

    Liu, Bolian (et al.)

    Pages 1-46

  • Combinatorial Properties of Matrices

    Liu, Bolian (et al.)

    Pages 47-96

  • Powers of Nonnegative Matrices

    Liu, Bolian (et al.)

    Pages 97-159

  • Matrices in Combinatorial Problems

    Liu, Bolian (et al.)

    Pages 161-216

  • Combinatorial Analysis in Matrices

    Liu, Bolian (et al.)

    Pages 217-274

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-1-4757-3165-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-0-7923-6469-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-1-4419-4834-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Matrices in Combinatorics and Graph Theory
Authors
Series Title
Network Theory and Applications
Series Volume
3
Copyright
2000
Publisher
Springer US
Copyright Holder
The Editor(s) (if applicable) and The Author(s) 2018
eBook ISBN
978-1-4757-3165-1
DOI
10.1007/978-1-4757-3165-1
Hardcover ISBN
978-0-7923-6469-6
Softcover ISBN
978-1-4419-4834-2
Series ISSN
1568-1696
Edition Number
1
Number of Pages
XI, 310
Topics