Skip to main content

Advertisement

SpringerLink
Log in

On energies of non-extended P-sum of cyclic graphs

  • Regular Article
  • Published:
The European Physical Journal Plus Aims and scope Submit manuscript

Abstract

Let G be the graph and the energy of graph G is depend on the summation of its absolute eigenvalues. We study the Randic, Seidel,and Laplacian energies of graph G where G is the non-extended p-sum of the graphs. We show that the energy of graph is depend on the base elements and how this result is used to generalize the concept of energies. We are interested in computing the energies for NEPS of graph \(G_{i}\) where \(G_{i}\) is the cyclic graph \(C_{i}\) for different values of i.

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
Fig. 2
Fig. 3

Similar content being viewed by others

References

  1. X. Li, I. Gutman, Mathematical Aspects of Randić -type Molecular Structure Descriptors (Univ, Kragujevac, Kragujevac, 2006)

  2. B.J. McClelland, Properties of the latent roots of a matrix: the estimation of \(\pi \)-electron energies. J. Chem. Phys. 54, 640–643 (1971)

    Article  ADS  Google Scholar 

  3. I. Gutman, Acyclic systems with extremal Huckel \(\pi \)-electron energy. Theoret. Chim. Acta 45, 79–87 (1977)

    Article  Google Scholar 

  4. I. Gutman, The energy of a graph: old and new results, in textitAlgebraic Combinatorics and Applications, ed. by A. Betten, A. Kohnert, R. Laue and A.Wassermann, Eds, (Springer, 2001), pp. 196–211

  5. I. Gutman, X. Li, J. Zhang, Graph energy, in Analysis of Complex etworks. From Biology to Linguistics,ed by M. Dehmer and F. Emmert-Streib, Eds., (Wiley, 2009), pp. 145–174

  6. I. Gutman, B. Furtula, S. Burcu Bozkurt, On randic energy. Linear Multilinear Algebr. 442, 50–57 (2014)

    Article  MathSciNet  Google Scholar 

  7. M. Randić, On history of the randić index and emerging hostility toward chemical graph theory. MATCH Commun. Math. Comput. Chem. 59, 115–124 (2008)

    MATH  Google Scholar 

  8. M. Randic, On characterization of molecular branching. J. Am. Chem. Soc. 97, 6609–6615 (1975)

    Article  Google Scholar 

  9. X. Li, Y. Shi, A survey on the randić index. MATCH Commun. Math. Comput. Chem. 59, 127–156 (2008)

    MathSciNet  MATH  Google Scholar 

  10. W.H. Haemers, Seidel switching and graph energy. MATH Commun. Math. Comput. Chem 68, 653–659 (2012)

    MathSciNet  MATH  Google Scholar 

  11. M.R. Oboudi, Energy and seidel energy of graphs. MATCH Commun. Math. Comput. Chem. 75, 291–303 (2016)

    MathSciNet  MATH  Google Scholar 

  12. A. Chang, B. Deng, On the Laplacian energy of trees with perfect matchings. MATCH Commun. Math. Comput. Chem. 68, 767–776 (2012)

    MathSciNet  MATH  Google Scholar 

  13. B. Zhou, I. Gutman, T. Aleksić, A note on Laplacian energy of graphs. MATCH Commun. Math. Comput. Chem. 60, 441–446 (2008)

    MathSciNet  MATH  Google Scholar 

  14. B. Zhou, I. Gutman, On Laplacian energy of graphs. MATCH Commun. Math. Comput. Chem. 57, 211–220 (2008)

    MathSciNet  MATH  Google Scholar 

  15. B. Zhou, On Laplacian eigenvalues of a graph. Z. Nat. forsch. 59, 181–184 (2004)

    ADS  Google Scholar 

  16. C.T.M. Vinagre, R.R. Del-Vecchio, D.A.R. Justo, V. Trevisan, Maximum Laplacian energy among threshold graphs. Linear Algebr. Appl. 439, 1479–1495 (2013)

    Article  MathSciNet  Google Scholar 

  17. B. Zhou, New upper bounds for Laplacian energy. MATCH Commun. Math. Comput. Chem. 62, 553–560 (2009)

    MathSciNet  MATH  Google Scholar 

  18. M. Robbiano, E.A. Martins, R. Jiménez, B. San Martin, Upper bounds on the Laplacian energy of some graphs. MATCH Commun. Math. Comput. Chem. 64, 97–110 (2010)

  19. M. Robbiano, R. Jiménez, Applications of a theorem by Ky Fan in the theory of Laplacian energy of graphs. MATCH Commun. Math. Comput. Chem. 62, 537–552 (2009)

    MathSciNet  MATH  Google Scholar 

  20. H. Zhang, X. Bai, H. Zheng, H. Zhao, J. Zhou, J. Cheng, H. Lu, Hierarchical remote sensing image analysis via graph Laplacian energy. IEEE Geosci. Remote Sensing Lett. 10, 396–400 (2013)

    Article  ADS  Google Scholar 

  21. Y.Z. Song, P. Arbelaez, P. Hall, C. Li, A. Balikai, Finding semantic structures in image hierarchies using Laplacian graph energy, in 11th European Conference on Computer Vision, ECCV 2010, September 5, 2010 -September 11, 2010. ed. by K. Daniilidis, P. Maragos, N. Paragios (Part IV, Springer-Verlag, Berlin, 2010), pp. 694–707

  22. M. E. Bolaños, S. Aviyente, Quantifying the functional importance of neuronal assemblies in the brain using Laplacian Hückel graph energy, in Proceedings of International Conference on Acoustics, Speech and Signal Processing, vol. 18 (Prague, 2007), pp. 753–756

  23. S. Dragon, Energy and NEPS of graphs. Linear Multilinear Algebr. 53(1), 67–74 (2005)

    Article  MathSciNet  Google Scholar 

  24. I. Gutman, The energy of a graph. Ber. Math. Statist. Sekt. Forschungszentrum Graz. 103, 1–22 (1978)

    MATH  Google Scholar 

  25. R. Balakrishnan, The energy of a graph. Linear Algebr. Appl. 387, 287–295 (2004)

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful to the anonymous referee for their valuable comments and suggestions that improved this paper.

Author information

Authors and Affiliations

  1. School of Computer Science Chengdu University, Chengdu, China

    Rongbing Huang

  2. Department of Mathematics, Comsats University Islamabad, Lahore Campus, Lahore, Pakistan

    Sarfraz Ahmad, Muhammad Kamran Siddiqui, Iqra Farman & Yousaf Habib

Authors
  1. Rongbing Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sarfraz Ahmad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muhammad Kamran Siddiqui
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Iqra Farman
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Yousaf Habib
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Huang, R., Ahmad, S., Siddiqui, M.K. et al. On energies of non-extended P-sum of cyclic graphs. Eur. Phys. J. Plus 137, 237 (2022). https://doi.org/10.1140/epjp/s13360-022-02449-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjp/s13360-022-02449-5

Search

Navigation