Inverse eigenvalue and related problems for hollow matrices described by graphs

Journal Article (2022)
Author(s)

F.S. Dahlgren (Georgia State University, TU Delft - Network Architectures and Services)

Zachary Gershkoff (Louisiana State University)

Leslie Hogben (Iowa State University, American Institute of Mathematics)

Sara Motlaghian (Georgia State University)

Derek Young (Mount Holyoke College)

Research Group
Network Architectures and Services
Copyright
© 2022 F.S. Dahlgren, Zachary Gershkoff, Leslie Hogben, Sara Motlaghian, Derek Young
DOI related publication
https://doi.org/10.13001/ela.2022.6941
More Info
expand_more
Publication Year
2022
Language
English
Copyright
© 2022 F.S. Dahlgren, Zachary Gershkoff, Leslie Hogben, Sara Motlaghian, Derek Young
Research Group
Network Architectures and Services
Volume number
38
Pages (from-to)
661-679
Reuse Rights

Other than for strictly personal use, it is not permitted to download, forward or distribute the text or part of it, without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license such as Creative Commons.

Abstract

A hollow matrix described by a graph G is a real symmetric matrix having all diagonal entries equal to zero and with the off-diagonal entries governed by the adjacencies in G. For a given graph G, the determination of all possible spectra of matrices associated with G is the hollow inverse eigenvalue problem for G. Solutions to the hollow inverse eigenvalue problems for paths and complete bipartite graphs are presented. Results for related subproblems such as possible ordered multiplicity lists, maximum multiplicity of an eigenvalue, and minimum number of distinct eigenvalues are presented for additional families of graphs.