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Inverse Problems and Zero Forcing for Graphs

Leslie Hogben Iowa State University, Ames, IA and American Institute of Mathematics, San Jose, CA
Jephian C.-H. Lin National Sun Yat-sen University, Kaohsiung, Taiwan
Bryan L. Shader University of Wyoming, Laramie, WY
Available Formats:
Softcover ISBN: 978-1-4704-6655-8
Product Code: SURV/270
List Price: $125.00 MAA Member Price:$112.50
AMS Member Price: $100.00 Electronic ISBN: 978-1-4704-7137-8 Product Code: SURV/270.E List Price:$125.00
MAA Member Price: $112.50 AMS Member Price:$100.00
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $187.50 MAA Member Price:$168.75
AMS Member Price: $150.00 Click above image for expanded view Inverse Problems and Zero Forcing for Graphs Leslie Hogben Iowa State University, Ames, IA and American Institute of Mathematics, San Jose, CA Jephian C.-H. Lin National Sun Yat-sen University, Kaohsiung, Taiwan Bryan L. Shader University of Wyoming, Laramie, WY Available Formats:  Softcover ISBN: 978-1-4704-6655-8 Product Code: SURV/270  List Price:$125.00 MAA Member Price: $112.50 AMS Member Price:$100.00
 Electronic ISBN: 978-1-4704-7137-8 Product Code: SURV/270.E
 List Price: $125.00 MAA Member Price:$112.50 AMS Member Price: $100.00 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$187.50 MAA Member Price: $168.75 AMS Member Price:$150.00
• Book Details

Mathematical Surveys and Monographs
Volume: 2702022; 287 pp
MSC: 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.

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
• 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

• Requests

Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Volume: 2702022; 287 pp
MSC: 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.

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