Inverse eigenvalue and related problems for hollow matrices described by graphs

F. Scott Dahlgren, Zachary Gershkoff, Leslie Hogben, Sara Motlaghian, Derek Young*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

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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.

Original languageEnglish
Pages (from-to)661-679
Number of pages19
JournalElectronic Journal of Linear Algebra
Publication statusPublished - 2022


  • Hollow matrix
  • Inverse eigenvalue problem
  • Maximum multiplicity
  • Maximum nullity
  • Minimum number of distinct eigenvalues
  • Minimum rank
  • Ordered multiplicity list


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