Skip to main content
Log in

Spectral Characterizations of the Corona of a Cycle and Two Isolated Vertices

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

Abstract

For a cycle C n , let C n ○ 2K 1 be the graph obtained from C n by attaching two pendant edges to each vertex of C n . In this paper, we prove that C n ○ 2K 1 is determined by its signless Laplacian spectrum when n ≠ 32, 64. We also show that C n ○ 2K 1 is determined by its Laplacian spectrum.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Boulet R.: Spectral characterizations of sun graphs and broken sun graphs. Discret. Math. Theor.Comput. Sci. 11, 149–160 (2009)

    MATH  MathSciNet  Google Scholar 

  2. Boulet R., Jouve B.: The lollipop is determined by its spectrum. Electron. J. Combin. 15, R74 (2008)

    MathSciNet  Google Scholar 

  3. Bu C., Zhou J.: Starlike trees whosemaximum degree exceed 4 are determined by their Q-spectra. Linear Algebra Appl. 436, 143–151 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  4. Bu C., Zhou J.: SignlessLaplacian spectral characterization of the cones over someregular graphs.. Linear Algebra Appl. 436, 3634–3641 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  5. Bu C., Zhou J., Li H.: Spectral determination of some chemical graphs. Filomat 26(6), 1121–1129 (2012)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  7. Cvetković D., Rowlinson P., Simić S.: An Introduction to the Theory of Graph Spectra. Cambridge University Press, Cambridge (2010)

    MATH  Google Scholar 

  8. Grone R., Merris R.: The Laplacian spectrum of a graph II. SIAM J. Discret. Math. 7, 221–229 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hoffman, A.J., Smith, J.H.: On the spectral radii of topological equivalent graphs. In: Fiedker, M. (ed.) Recent Advances i Graph Theory. Academia Praha, New York, pp. 273–281 (1975)

  10. Huang T., Liu C.: Spectral characterization of some generalized odd graphs.. Graphs Combin. 15, 195–209 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  11. Lin Y.Q., Shu J.L., Meng Y.: Laplacian spectrum characterization of extensions of vertices of wheel graphs and multi-fan graphs. Comput. Math. Appl. 60, 2003–2008 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  12. Mirzakhah M., Kiani D.: The sun graph is determined by its signless Laplacian spectrum. Electron. J. Linear Algebra. 20, 610–620 (2010)

    MATH  MathSciNet  Google Scholar 

  13. Oliveira C.S., Abreu de N.M.M., Jurkiewicz S.: The characteristic polynomial of the Laplacian of 326 graphs in (a, b)-linear classes. Linear Algebra Appl. 356, 113–121 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  14. Ramezani F., Tayfeh-Rezaie B.: Spectral characterization of some cubic graphs. Graphs Combin. 28, 869–876 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  15. Van Dam E.R., Haemers W.H.: Which graphs are determined by their spectrum?. Linear Algebra Appl. 373, 241–272 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  16. Van Dam E.R., Haemers W.H.: Developments on spectral characterizations of graphs. Discret. Math. 309, 576–586 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  17. Wang J.F., Huang Q., Belardo F., Li Marzi E.M.: On graphs whose signless Laplacian index does not exceed 4.5. Linear Algebra Appl. 431, 162–178 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  18. Wang W., Xu C.X.: On the spectral characterization of T-shape trees. Linear Algebra Appl. 414, 492–501 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  19. Zhou J., Bu C.: Laplacian spectral characterization of some graphs obtained by product operation. Discret. Math. 312, 1591–1595 (2012)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Changjiang Bu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bu, C., Zhou, J., Li, H. et al. Spectral Characterizations of the Corona of a Cycle and Two Isolated Vertices. Graphs and Combinatorics 30, 1123–1133 (2014). https://doi.org/10.1007/s00373-013-1327-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-013-1327-7

Keywords

Mathematics Subject Classification

Navigation