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.
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Zielgruppe
Maße
Höhe: 254 mm
Breite: 178 mm
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ISBN-13
978-1-4704-6655-8 (9781470466558)
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Schweitzer Klassifikation
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.
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
Rigid linkages
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
Bibliography
Index