Combinatorial Matrix Theory

by Richard A. Brualdi, ïngeles Carmona, P. van den Driessche, Stephen Kirkland, Dragan Stevanovic

Overview

This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.

Product Details

ISBN-13:	9783319709529
Publisher:	Springer International Publishing
Publication date:	04/01/2018
Series:	Advanced Courses in Mathematics - CRM Barcelona
Edition description:	1st ed. 2018
Pages:	219
Product dimensions:	6.61(w) x 9.45(h) x (d)

About the Author

Richard A. Brualdi is an Emeritus Professor at the University of Wisconsin in Madison, WI, USA.

Pauline van den Driessche is an Emeritus Professor at the University of Victoria, Canada.

Dragan Stevanović is a Full Research Professor at the Serbian Academy of Sciences and Arts in Belgrade, Serbia.

Stephen Kirkland is a Professor at the University of Manitoba in Winnipeg, Canada.

Ángeles Carmona is an Associate Professor at the Universitat Politècnica de Catalunya in Barcelona, Spain.

Table of Contents

Some combinatorially defined matrix class.- Sign pattern matrices.- The spectral radius of a graph.- The group inverse of the Laplacian matrix of a graph.- Boundary value problems on finite networks.

Editorial Reviews

"A reader who is familiar with basic results in matrix theory will surely be captivated by this concise self-contained introduction to graph theory and combinatorial ideas and reasoning." S. K. Tharthare, Mathematical Reviews

"...a major addition to the literature of combinatorics." W. T. Tutte, Bulletin of the American Mathematical Society

From the Publisher