Skip to main content
SpringerLink
Log in

An Inverse Eigenvalue Problem for Symmetric Acyclic Matrices: The Case of Generalized Star Graph

  • Research Paper
  • Published:
Iranian Journal of Science Aims and scope Submit manuscript

Abstract

Constructing a matrix with a specific structure from prescribed spectral data is known as an inverse eigenvalue problem. In this paper, an inverse eigenvalue problem for a special kind of symmetric acyclic matrices whose graph is a generalized star graph is considered. The inverse problem is to construct matrices of this kind by one eigenpair and one of the eigenvalues of all trailing principal submatrices. The sufficient conditions for the solvability of the problem are derived. Furthermore, we provide an algorithmic procedure that is illustrated in a numerical example.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Algorithm 1

Similar content being viewed by others

References

  • Ayatollahi M (2013) Maximal and minimal eigenvalue assignment for discrete-time periodic systems by state feedback. Optim Lett 7(6):1119–1123

    Article  MathSciNet  Google Scholar 

  • Chu M, Golub G (2005) Inverse eigenvalue problems: theory, algorithms, and applications. Numerical Mathematics and Scientific. Oxford University Press, Oxford

    Book  Google Scholar 

  • Heydari M, Fazeli SAS, Karbassi SM (2019) On the inverse eigenvalue problem for a special kind of acyclic matrices. Appl Math 64(2):351–366

    Article  MathSciNet  Google Scholar 

  • Heydari M, Fazeli SAS, Karbassi SM, Hooshmandasl MR (2020) On the inverse eigenvalue problem for periodic Jacobi matrices. Inverse Prob Sci Eng 28(9):1253–1264

    Article  MathSciNet  Google Scholar 

  • Hogben L (2005) Spectral graph theory and the inverse eigenvalue problem of a graph. Electronic J Linear Algebra 14:12–31

    Article  MathSciNet  Google Scholar 

  • Johnson CR, Saiago ALDCM (2003) Inverse eigenvalue problems and lists of multiplicities of eigenvalues for matrices whose graph is a tree: the case of generalized stars and double generalized stars. Linear Algebra Appl 373(2):311–330

    Article  MathSciNet  Google Scholar 

  • Nylen P, Uhlig F (1997) Inverse eigenvalue problems associated with spring-mass systems. Linear Algebra Appl 254(1):409–425

    Article  MathSciNet  Google Scholar 

  • Peng J, Hu X-Y, Zhang L (2006) Two inverse eigenvalue problems for a special kind of matrices. Linear Algebra Appl 416:336–347

    Article  MathSciNet  Google Scholar 

  • Sharma D, Sarma BK (2022) Extremal inverse eigenvalue problem for irreducible acyclic matrices. Appl Math Sci Eng 30(1):192–209

    Article  MathSciNet  Google Scholar 

  • Sharma D, Sen M (2018) Inverse eigenvalue problems for acyclic matrices whose graph is a dense centipede. Special Matrices 6(1):77–92

    Article  MathSciNet  Google Scholar 

  • Sharma D, Sen M (2016) Inverse eigenvalue problems for two special acyclic matrices. Mathematics 4(1)

  • Xu WR, Chen GL (2017) On inverse eigenvalue problems for two kinds of special banded matrices. Filomat 31(2):371–385

    Article  MathSciNet  Google Scholar 

Download references

Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

Author information

Authors and Affiliations

  1. Department of Computer Science, Khansar Campus, University of Isfahan, Isfahan, Iran

    Mohammad Heydari

  2. Department of Mathematics, Dezful Branch, Islamic Azad University, Dezful, Iran

    Ferya Fathi

Authors
  1. Mohammad Heydari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ferya Fathi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Heydari.

Ethics declarations

Conflict of interest

The authors have no relevant financial or non-financial interests to disclose.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Heydari, M., Fathi, F. An Inverse Eigenvalue Problem for Symmetric Acyclic Matrices: The Case of Generalized Star Graph. Iran J Sci (2024). https://doi.org/10.1007/s40995-024-01605-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40995-024-01605-z

Keywords

Search

Navigation