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.
| ISBN: | 9781470466558 |
| Publication date: | 30th October 2022 |
| Author: | Leslie Hogben, Jephian CH Lin, Bryan L Shader |
| Publisher: | American Mathematical Society |
| Format: | Paperback |
| Pagination: | 286 pages |
| Series: | Mathematical Surveys and Monographs |
| Genres: |
Discrete mathematics Combinatorics and graph theory |