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Inverse Problems and Zero Forcing for Graphs.
・ISBN 978-1-4704-6655-8 paper US$ 125.00
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| 著者・編者 | Hogben, Leslie / Lin, Jephian C.-H. / Shader, Bryan L., |
|---|---|
| シリーズ | Mathematical Surveys and Monographs |
| 出版社 | (American Mathematical Society, US) |
| 出版年月 | 2022 |
| ページ数 | 286 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-6774＞ |
解説
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.
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.