Skip to main content
SpringerLink
Log in

Some further bounds for the Q-index of nested split graphs

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

The Q-index of a simple graph is the largest eigenvalue of its signless Laplacian, or Q-matrix. In our previous paper [1] we gave three lower and three upper bounds for the Q-index of nested split graphs, also known as threshold graphs. In this paper, we give another two upper bounds, which are expressed as solutions of cubic equations (in contrast to quadratics from [1]). Some computational results are also included.

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

Similar content being viewed by others

References

  1. M. Anđelić, C. M. da Fonseca, S. K. Simić, and D. V. Tošić, “Connected graphs of fixed order and size with maximal Q-index: Some spectral bounds,” (to be published).

  2. M. Anđelić and S. K. Simić, “Some notes on threshold graphs,” Discr. Math., 310, 2241–2248 (2010).

    Article  MATH  Google Scholar 

  3. D. Cvetković, P. Rowlinson, and S. Simić, “Signless Laplacians of finite graphs,” Linear Algebra Appl., 423, No. 1, 155–171 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  4. D. Cvetković, P. Rowlinson, and S. Simić, “Eigenvalue bounds for the signless Laplacian,” Publ. Inst. Mat. Beograd, 81 (95), 11–27 (2007).

    Article  Google Scholar 

  5. D. Cvetković, P. Rowlinson, and S. Simić, An Introduction to the Theory of Graph Spectra, Cambridge Univ. Press, Cambridge (2010).

    MATH  Google Scholar 

  6. D. Cvetković and S. K. Simić, “Towards a spectral theory of graphs based on the signless Laplacian, I,” Publ. Inst. Mat. Beograd, 85 (99), 19–33 (2009).

    Article  Google Scholar 

  7. D. Cvetković and S. K. Simić, “Towards a spectral theory of graphs based on the signless Laplacian, II,” Linear Algebra Appl., 432, No. 9, 2257–2272 (2010).

    Article  MathSciNet  MATH  Google Scholar 

  8. D. Cvetković and S. K. Simić, “Towards a spectral theory of graphs based on the signless Laplacian, III,” Appl. Anal. Discr. Math., 4, 156–166 (2010).

    Article  Google Scholar 

  9. L. Feng and G. Yu, “On three conjectures involving the signless Laplacian spectral radius of graphs,” Publ. Inst. Mat. Beograd, 85 (99), 35–38(2009).

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    M. Anđelić

  2. Department of Mathematics, University of Coimbra, Coimbra, Portugal

    C. M. da Fonseca

  3. Mathematical Institute SANU, Belgrade, Serbia

    S. K. Simić

  4. School of Electrical Engineering, University of Belgrade, Belgrade, Serbia

    D. V. Tošić

Authors
  1. M. Anđelić
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. C. M. da Fonseca
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. K. Simić
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. D. V. Tošić
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Anđelić.

Additional information

Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 71, Algebraic Techniques in Graph Theory and Optimization, 2011.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Anđelić, M., da Fonseca, C.M., Simić, S.K. et al. Some further bounds for the Q-index of nested split graphs. J Math Sci 182, 193–199 (2012). https://doi.org/10.1007/s10958-012-0739-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-012-0739-x

Keywords

Search

Navigation