# Matrices in Combinatorics and Graph Theory

Book

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

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

### 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

1. 1.Department of MathematicsSouth China Normal UniversityGuangzhouP.R. China
2. 2.Department of MathematicsWest Virginia UniversityMorgantownUSA

### Bibliographic information

• Book Title Matrices in Combinatorics and Graph Theory
• Authors Bolian Liu
Hong-Jian Lai
• Series Title Network Theory and Applications
• DOI https://doi.org/10.1007/978-1-4757-3165-1
• Copyright Information Springer-Verlag US 2000
• Publisher Name Springer, Boston, MA
• eBook Packages
• Hardcover ISBN 978-0-7923-6469-6
• Softcover ISBN 978-1-4419-4834-2
• eBook ISBN 978-1-4757-3165-1
• Series ISSN 1568-1696
• Edition Number 1
• Number of Pages XI, 310
• Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
• Topics
• Buy this book on publisher's site
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