Inverse eigenvalue and related problems for hollow matrices described by graphs

Journal article (2022)

Authors

F.S. Dahlgren Georgia State University, Network Architectures and Services - EEMCS
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 (EEMCS) (TU Delft)
Copyright: © 2022 F.S. Dahlgren, Zachary Gershkoff, Leslie Hogben, Sara Motlaghian, Derek Young
DOI: https://doi.org/10.13001/ela.2022.6941
Hollow matrix Inverse eigenvalue problem Maximum multiplicity Maximum nullity Minimum number of distinct eigenvalues Minimum rank Ordered multiplicity list
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Published Date

2022

Language

English

Faculty

Electrical Engineering, Mathematics and Computer Science

Department

Quantum & Computer Engineering

Research Group

Network Architectures and Services

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.