Matrices in Combinatorics and Graph Theory

Liu, Bolian; Lai, Hong-Jian

ISBN 10: 0792364694 / ISBN 13: 9780792364696

Published by Kluwer Academic Publishers, 2000

About this Item

Providing a brief treatment of the basics of the subject, this work includes chapters that deal with the various decompositions of non-negative matrices, Birkhoff type theorems, the study of the powers of non-negative matrices, and applications of matrix methods to other combinatorial problems. Series: Network Theory and Applications. Num Pages: 310 pages, biography. BIC Classification: PBF. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly. Dimension: 235 x 155 x 19. Weight in Grams: 636. . 2000. 2000th Edition. hardcover. . . . .

Seller Inventory # V9780792364696

Bibliographic Details

• Title: Matrices in Combinatorics and Graph Theory
• Publisher: Kluwer Academic Publishers
• Publication Date: 2000
• Language: English
• ISBN 10: 0792364694
• ISBN 13: 9780792364696
• Binding: Hardcover
• Condition: New

About this title

Synopsis

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.

Synopsis

The first chapter of this book provides a brief treatment of the basics of the subject. The other chapters deal with the various decompositions of non-negative matrices, Birkhoff type theorems, the study of the powers of non-negative matrices, applications of matrix methods to other combinatorial problems, and applications of combinatorial methods to matrix problems and linear algebra problems. The coverage of prerequisites has been kept to a minimum. Nevertheless, the book is basically self-contained (an Appendix provides the necessary background in linear algebra, graph theory and combinatorics). There are many exercises, all of which are accompanied by sketched solutions. The book is suitable for a graduate course as well as being an excellent reference and a valuable resource for mathematicians working in the area of combinatorial matrix theory.