Construction of matrices with a given graph and prescribed interlaced spectral data

Monfared, Keivan Hassani; Shader, Bryan L.

doi:10.1016/j.laa.2013.01.036

Cited by 24 publications

(7 citation statements)

References 11 publications

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“…Therefore, by Theorem 2.10, every graph on n vertices has a realization that is cospectral with D and has the SSP. The existence of a cospectral matrix was proved in [24] via a different method.…”

Section: The Strong Spectral Propertymentioning

confidence: 99%

Generalizations of the Strong Arnold Property and the Minimum Number of Distinct Eigenvalues of a Graph

Barrett

Fallat

Hall

et al. 2017

Electron. J. Combin.

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For a given graph G and an associated class of real symmetric matrices whose offdiagonal entries are governed by the adjacencies in G, the collection of all possible spectra for such matrices is considered. Building on the pioneering work of Colin de Verdière in connection with the Strong Arnold Property, two extensions are devised that target a better understanding of all possible spectra and their associated multiplicities. These new properties are referred to as the Strong Spectral Property and the Strong Multiplicity Property. Finally, these ideas are applied to the minimum number of distinct eigenvalues associated with G, denoted by q(G). The graphs for which q(G) is at least the number of vertices of G less one are characterized.

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Section: The Strong Spectral Propertymentioning

confidence: 99%

Generalizations of the Strong Arnold Property and the Minimum Number of Distinct Eigenvalues of a Graph

Barrett

Fallat

Hall

et al. 2017

Electron. J. Combin.

Self Cite

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“…In [1], Chu and Golub gave a very perfect characterization of IEPs. IEPs have many practical applications such as control theory, mechanical system simulation, geophysics, molecular spectroscopy, structural analysis, mass spring vibrations, circuit theory and graph theory [1], [5], [6].…”

Section: Introductionmentioning

confidence: 99%

On the inverse eigenvalue problem for a special kind of acyclic matrices

2019

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“…It is interesting to consider IEPs which require the construction of matrices having a pre-assigned pattern of zero entries. Eigenvalue problems for matrices with prescribed graphs have also been studied in the literature [2,3,10,13,14]. IEPs concerning the reconstruction of special acyclic matrices like path and broom, from given eigen data have been studied in [17,18].…”

Section: Introductionmentioning

confidence: 99%

“…IEPs concerning the reconstruction of special acyclic matrices like path and broom, from given eigen data have been studied in [17,18]. Inverse eigenvalue problems arise in a number of appli-cations such as control theory, pole assignment problems, system identi cation, structural analysis, mass spring vibrations, circuit theory, mechanical system simulation and graph theory [1,9,13,15]. Thus, methods for constructing matrices of various structures from various types of eigen data are indeed useful.…”

Section: Introductionmentioning

confidence: 99%

Inverse eigenvalue problems for acyclic matrices whose graph is a dense centipede

Sharma

Sen

2018

Special Matrices

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Abstract:The reconstruction of a matrix having a pre-de ned structure from given spectral data is known as an inverse eigenvalue problem (IEP). In this paper, we consider two IEPs involving the reconstruction of matrices whose graph is a special type of tree called a centipede. We introduce a special type of centipede called dense centipede. We study two IEPs concerning the reconstruction of matrices whose graph is a dense centipede from given partial eigen data. In order to solve these IEPs, a new system of nomenclature of dense centipedes is developed and a new scheme is adopted for labelling the vertices of a dense centipede as per this nomenclature . Using this scheme of labelling, any matrix of a dense centipede can be represented in a special form which we de ne as a connected arrow matrix. For such a matrix, we derive the recurrence relations among the characteristic polynomials of the leading principal submatrices and use them to solve the above problems. Some numerical results are also provided to illustrate the applicability of the solutions obtained in the paper.

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Construction of matrices with a given graph and prescribed interlaced spectral data

Cited by 24 publications

References 11 publications

Generalizations of the Strong Arnold Property and the Minimum Number of Distinct Eigenvalues of a Graph

Generalizations of the Strong Arnold Property and the Minimum Number of Distinct Eigenvalues of a Graph

On the inverse eigenvalue problem for a special kind of acyclic matrices

Inverse eigenvalue problems for acyclic matrices whose graph is a dense centipede

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