Skip to main content
SpringerLink
Log in

Kirchhoff Index for Circulant Graphs and Its Asymptotics

  • MATHEMATICS
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

The aim of this paper is to find an analytical formula for the Kirchhoff index of circulant graphs \({{C}_{n}}({{s}_{1}},{{s}_{2}},\; \ldots ,\;{{s}_{k}})\) and \({{C}_{{2n}}}({{s}_{1}},{{s}_{2}},\; \ldots ,\;{{s}_{k}},n)\) with even and odd valency, respectively. The asymptotic behavior of the Kirchhoff index as n → ∞ is investigated. We proof that the Kirchhoff index of a circulant graph can be expressed as a sum of a cubic polynomial in n and a quantity that vanishes exponentially as n → ∞.

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. B. Mohar, in Graph Theory, Combinatorics, and Applications, Ed. by Y. Alavi, G. Chartrand, O. R. Oellermann, and A. J. Schwenk (Wiley, New York, 1991), Vol. 2, pp. 871–898.

    Google Scholar 

  2. D. J. Klein and M. Randić, J. Math. Chem. 12, 81–95 (1993).

    Article  MathSciNet  Google Scholar 

  3. H. Wiener, J. Am. Chem. Soc. 1 (69), 17–20 (1947).

    Article  Google Scholar 

  4. I. Gutman and B. Mohar, J. Chem. Inf. Comput. Sci. 36, 982–985 (1996).

    Article  Google Scholar 

  5. H. Y. Zhu, D. J. Klein, and I. Lukovits, Chem. Inf. Comput. Sci. 36 (3), 420–428 (1996).

    Article  Google Scholar 

  6. I. Lukovits, S. Nikolić, and N. Trinajstić, Int. J. Quantum Chem. 71, 217–225 (1999).

    Article  Google Scholar 

  7. J. L. Palacios, Int. J. Quantum Chem. 81, 135–140 (2001).

    Article  Google Scholar 

  8. H. Zhang and Y. Yang, Int. J. Quantum Chem. 107, 330–339 (2007).

    Article  Google Scholar 

  9. W. Xiao and I. Gutman, Theor. Chem. Acc. 110, 284–289 (2009).

    Article  Google Scholar 

  10. L. Ye, Linear Multilinear Algebra 59 (6), 645–650 (2011).

    Article  MathSciNet  Google Scholar 

  11. Z. Cinkir, J. Math. Chem. 54 (4), 955–966 (2016).

    Article  MathSciNet  Google Scholar 

  12. M. Kagan and B. Mata, Math. Comput. Sci. 13, 105–115 (2019).

    Article  MathSciNet  Google Scholar 

  13. G. A. Baigonagova and A. D. Mednykh, Sib. Electron. Math. Rep. 16, 1654–1661 (2019).

    Google Scholar 

Download references

Funding

This work was supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation.

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    A. D. Mednykh & I. A. Mednykh

  2. Novosibirsk State University, 630090, Novosibirsk, Russia

    A. D. Mednykh & I. A. Mednykh

Authors
  1. A. D. Mednykh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. A. Mednykh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to A. D. Mednykh or I. A. Mednykh.

Additional information

Translated by I. Ruzanova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mednykh, A.D., Mednykh, I.A. Kirchhoff Index for Circulant Graphs and Its Asymptotics. Dokl. Math. 102, 392–395 (2020). https://doi.org/10.1134/S106456242005035X

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S106456242005035X

Keywords

Search

Navigation