Skip to main content
SpringerLink
Log in

On the Index of Necklaces

  • Original Paper
  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

We consider the following two classes of simple graphs: open necklaces and closed necklaces, consisting of a finite number of cliques of fixed orders arranged in path-like pattern and cycle-like pattern, respectively. In these two classes we determine those graphs whose index (the largest eigenvalue of the adjacency matrix) is maximal.

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. Belardo F., Li Marzi E.M., Simić S.K.: Some results on the index of unicyclic graphs. Linear Algebra Appl. 416(2–3), 1048–1059 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Biyikoğlu, T., Leydold, J.: Graphs with given degree sequence and maximal spectral radius. Electron. J. Combin. 15, #R119 (2008)

  3. Biyikoğlu, T., Leydold, J.: Semiregular trees with minimal Laplacian spectral radius. Linear Algebra Appl. (2009, in press). doi:10.1016/j.laa.2009.06.014

  4. Cvetković, D., Doob, M., Sachs, H.: Spectra of Graphs—Theory and Applications, III revised and enlarged edition. Johan Ambrosius Bart. Verlag, Heidelberg (1995)

  5. Cvetković D., Rowlinson P., Simić S.: Eigenspaces of Graphs. Cambridge University Press, Cambridge (1997)

    MATH  Google Scholar 

  6. Cvetković D., Rowlinson P., Simić S.K.: Signless Laplacians of finite graphs. Linear Algebra Appl. 423(1), 155–171 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  7. Cvetković D., Simić S.K.: Towards a spectral theory of graphs based on the signless Laplacian. I. Publ. Math. Inst. (Beograd), Nouvelle Série 85(99), 19–33 (2009)

    Google Scholar 

  8. Cvetković, D., Simić, S.K.: Towards a spectral theory of graphs based on the signless Laplacian, II. Linear Algebra Appl. (2009, in press). doi:10.1016/j.laa.2009.05.020

  9. Harary F.: Graph Theory. Addison-Wesley, Reading (1969)

    Google Scholar 

  10. Hoffman A.J., Smith J.H.: On the spectral radii of topologically equivalent graphs. In: Fiedler, M. (eds) Recent Advances in Graph Theory, pp. 273–281. Academia Praha, Prague (1975)

    Google Scholar 

  11. Merris R.: Laplacian matrices of graphs. Linear Algebra Appl. 197(198), 143–176 (1994)

    Article  MathSciNet  Google Scholar 

  12. Simić S.K., Li Marzi E.M., Belardo F.: On the index of caterpillars. Discrete Math. 308, 324–330 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  13. Yuan, X.Y., Wu, B.F., Xiao, E.L.: The modifications of trees and the Laplacian spectrum. J. East China Norm. Univ. Natur. Sci. (in Chinese), Ed. June (2), pp. 13–18 (2004)

  14. Zhang X.D.: The Laplacian spectral radii of trees with degree sequences. Discrete Math. 308, 3143–3150 (2008)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Messina, Messina, Italy

    Francesco Belardo & Enzo M. Li Marzi

  2. Mathematical Institute SANU, Belgrade, Serbia

    Slobodan K. Simić

  3. Department of Mathematics and Information Science, Qinghai Normal University, Xining, Qinghai, People’s Republic of China

    Jianfeng Wang

Authors
  1. Francesco Belardo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Enzo M. Li Marzi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Slobodan K. Simić
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jianfeng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Francesco Belardo.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belardo, F., Li Marzi, E.M., Simić, S.K. et al. On the Index of Necklaces. Graphs and Combinatorics 26, 163–172 (2010). https://doi.org/10.1007/s00373-010-0910-4

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-010-0910-4

Keywords

Mathematics Subject Classification (2000)

Search

Navigation