Shader, Bryan L.（著者）：University of Wyoming, Laramie, WY

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.