Combinatorial Matrix Theory

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This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matem輆ica (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 聲geles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.


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Chapter 1 Some Combinatorially Defined Matrix Classes
Chapter 2 Sign Pattern Matrices
Chapter 3 Spectral Radius of Graphs
Chapter 4 The Group Inverse of the Laplacian Matrix of a Graph
Chapter 5 Boundary Value Problems on Finite Networks

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About the author (2018)

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.

聲geles Carmona is an Associate Professor at the Universitat Polit鋃nica de Catalunya in Barcelona, Spain.