Softcover ISBN:  9781470466558 
Product Code:  SURV/270 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 
Electronic ISBN:  9781470471378 
Product Code:  SURV/270.E 
List Price:  $125.00 
MAA Member Price:  $112.50 
AMS Member Price:  $100.00 

Book DetailsMathematical Surveys and MonographsVolume: 270; 2022; 287 ppMSC: Primary 05; 15;
This book provides an introduction to the inverse eigenvalue problem for graphs (IEP\(G\)) and the related area of zero forcing, propagation, and throttling. The IEP\(G\) grew from the intersection of linear algebra and combinatorics and has given rise to both a rich set of deep problems in that area as well as a breadth of “ancillary” problems in related areas.
The IEP\(G\) asks a fundamental mathematical question expressed in terms of linear algebra and graph theory, but the significance of such questions goes beyond these two areas, as particular instances of the IEP\(G\) also appear as major research problems in other fields of mathematics, sciences and engineering. One approach to the IEP\(G\) is through rank minimization, a relevant problem in itself and with a large number of applications. During the past 10 years, important developments on the rank minimization problem, particularly in relation to zero forcing, have led to significant advances in the IEP\(G\).
The monograph serves as an entry point and valuable resource that will stimulate future developments in this active and mathematically diverse research area.ReadershipGraduate students and researchers interested in inverse eigenvalue problems for graph and rank minimization.

Table of Contents

Introduction to the inverse eigenvalue problem of a graph and zero forcing

Introduction to an motivation for the IEP$G$

Zero forcing and maximum eigenvalue multiplicity

Strong properties, theory, and consequences

Implicit function theorem and strong properties

Consequences of the strong properties

Theoretical underpinnings of the strong properties

Further discussion of ancillary problems

Ordered multiplicity lists of a graph

Rigid linkages

Minimum number of district eigenvalues

Zero forcing, propagation time, and throttling

Zero forcing, variants, and related parameters

Propagation time and capture time

Throttling

Appendix A. Graph terminology and notation


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This book provides an introduction to the inverse eigenvalue problem for graphs (IEP\(G\)) and the related area of zero forcing, propagation, and throttling. The IEP\(G\) grew from the intersection of linear algebra and combinatorics and has given rise to both a rich set of deep problems in that area as well as a breadth of “ancillary” problems in related areas.
The IEP\(G\) asks a fundamental mathematical question expressed in terms of linear algebra and graph theory, but the significance of such questions goes beyond these two areas, as particular instances of the IEP\(G\) also appear as major research problems in other fields of mathematics, sciences and engineering. One approach to the IEP\(G\) is through rank minimization, a relevant problem in itself and with a large number of applications. During the past 10 years, important developments on the rank minimization problem, particularly in relation to zero forcing, have led to significant advances in the IEP\(G\).
The monograph serves as an entry point and valuable resource that will stimulate future developments in this active and mathematically diverse research area.
Graduate students and researchers interested in inverse eigenvalue problems for graph and rank minimization.

Introduction to the inverse eigenvalue problem of a graph and zero forcing

Introduction to an motivation for the IEP$G$

Zero forcing and maximum eigenvalue multiplicity

Strong properties, theory, and consequences

Implicit function theorem and strong properties

Consequences of the strong properties

Theoretical underpinnings of the strong properties

Further discussion of ancillary problems

Ordered multiplicity lists of a graph

Rigid linkages

Minimum number of district eigenvalues

Zero forcing, propagation time, and throttling

Zero forcing, variants, and related parameters

Propagation time and capture time

Throttling

Appendix A. Graph terminology and notation