## 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.

Original language | English |
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Pages (from-to) | 661-679 |

Number of pages | 19 |

Journal | Electronic Journal of Linear Algebra |

Volume | 38 |

DOIs | |

Publication status | Published - 2022 |

## Keywords

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