Inverse Problems and Zero Forcing for Graphs (Mathematical Surveys and Monographs, 270)

By Leslie Hogben

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.

• Format: Paperback
• Language: English
• ISBN: 1470466554
• ISBN13: 9781470466558
• Release Date: July 2022
• Publisher: American Mathematical Society
• Length: 287 Pages
• Weight: 1.20 lbs.
• Dimensions: 10.0" x 0.8" x 7.0"