Skip to main content
Log in

Various energies of commuting graphs of some super integral groups

  • Original Research
  • Published:
Indian Journal of Pure and Applied Mathematics Aims and scope Submit manuscript

Abstract

A simple undirected graph \(\Gamma _G\) whose vertex set is the set of non-central elements of a finite group G and two vertices x and y are adjacent if they commute is called commuting graph of G. In this paper, we compute energy, Laplacian energy and signless Laplacian energy of \(\Gamma _G\) for some classes of super integral groups.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Abdollahi, S. M. Jafarain and A. M. Hassanabadi, Groups with specific number of centralizers, Houston J. Math., 33(1)(2007), 43–57.

    MathSciNet  MATH  Google Scholar 

  2. M. Afkhami, M. Farrokhi D. G. and K. Khashyarmanesh, Planar, toroidal, and projective commuting and non-commuting graphs, Comm. Algebra, 43(7)(2015), 2964–2970.

  3. S. Akbari, A. Mohammadian, H. Radjavi and P. Raja, On the diameters of commuting graphs, Linear Algebra Appl., 418(2006), 161–176.

    Article  MathSciNet  Google Scholar 

  4. S. M. Belcastro and G. J. Sherman, Counting centralizers in finite groups, Math. Magazine, 67(5)(1994), 366–374.

    Article  MathSciNet  Google Scholar 

  5. A. K. Das and D. Nongsiang, On the genus of the commuting graphs of finite non-abelian groups, Int. Electron. J. Algebra, 19(2016), 91–109.

    Article  MathSciNet  Google Scholar 

  6. J. Dutta and R. K. Nath, Finite groups whose commuting graphs are integral, Mat. Vesnik, 69(3)(2017), 226–230.

    MathSciNet  MATH  Google Scholar 

  7. J. Dutta and R. K. Nath, Spectrum of commuting graphs of some classes of finite groups, Matematika, 33(1)(2017), 87–95.

    Article  MathSciNet  Google Scholar 

  8. J. Dutta and R. K. Nath, Laplacian and signless Laplacian spectrum of commuting graphs of finite groups, Khayyam J. Math., 4(1)(2018), 77–87.

    MathSciNet  MATH  Google Scholar 

  9. G. L. Morgan and C. W. Parker, The diameter of the commuting graph of a finite group with trivial center, J. Algebra, 393(1)(2013), 41–59.

    Article  MathSciNet  Google Scholar 

  10. R. K. Nath, Various spectra of commuting graphs of n-centralizer finite groups, International J. Engineering, Science and Technology, 10(2S)(2018), 165–167.

    Google Scholar 

  11. R. Sharafdini, R. K. Nath and R. Darbandi, Energy of commuting graph of finite groups, https://arxiv.org/pdf/1704.06464.pdf.

Download references

Acknowledgements

The authors are grateful to the referee for his/her valuable comments. The authors would like to thank Mr. Rivu Bardhan, Mr. Biswadeep Bagchi and Ms. Walaa Fasfous for correcting some errors in an earlier version of this paper.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rajat Kanti Nath.

Additional information

Communicated by Sharad S Sane.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dutta, P., Nath, R.K. Various energies of commuting graphs of some super integral groups. Indian J Pure Appl Math 52, 1–10 (2021). https://doi.org/10.1007/s13226-021-00131-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13226-021-00131-7

Keywords

2010 Mathematics Subject Classification

Navigation