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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 494, Pages 43–47
DOI: https://doi.org/10.31857/S2686954320050379 (Mi danma115) 		 
This article is cited in 4 scientific papers (total in 4 papers)

MATHEMATICS

Kirchhoff index for circulant graphs and its asymptotics

A. D. Mednykhab, I. A. Mednykhab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russian Federation
b Novosibirsk State University, Novosibirsk, Russian Federation
Full-text PDF (160 kB) Citations (4)
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DOI: https://doi.org/10.31857/S2686954320050379
Abstract: The aim of this paper is to find an analytical formula for the Kirchhoff index of circulant graphs $C_n(s_1,s_2,\dots,s_k)$ and $C_{2n}(s_1,s_2,\dots,s_k,n)$ with even and odd valency, respectively. The asymptotic behavior of the Kirchhoff index as $n\to\infty$ 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 $n\to\infty$.
Keywords: circulant graph, Laplacian matrix, eigenvalue, Wiener index, Kirchhoff index.
Funding agency Grant number
Mathematical Center in Akademgorodok 075-15-2019-1613
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.
Presented: Yu. G. Reshetnyak
Received: 06.12.2019
Revised: 29.08.2020
Accepted: 31.08.2020
English version:
Doklady Mathematics, 2020, Volume 102, Issue 2, Pages 392–395
DOI: https://doi.org/10.1134/S106456242005035X
Bibliographic databases:
Document Type: Article
UDC: 517.545+517.962.2+519.173
Language: Russian
Citation: A. D. Mednykh, I. A. Mednykh, “Kirchhoff index for circulant graphs and its asymptotics”, Dokl. RAN. Math. Inf. Proc. Upr., 494 (2020), 43–47; Dokl. Math., 102:2 (2020), 392–395
Citation in format AMSBIB
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\pages 43--47
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\jour Dokl. Math.
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Linking options:
  • https://www.mathnet.ru/eng/danma115
  • https://www.mathnet.ru/eng/danma/v494/p43
    • This publication is cited in the following 4 articles:
    1. Y. S. Kwon, A. D. Mednykh, I. A. Mednykh, “On the Structure of Laplacian Characteristic Polynomial of Circulant Graphs”, Dokl. Math., 2024  crossref
    2. Y. S. Kwon, A. D. Mednykh, I. A. Mednykh, “On the structure of Laplacian characteristic polynomial of circulant graphs”, Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, 515:1 (2024), 34  crossref
    3. A. D. Mednykh, I. A. Mednykh, “The Kirchhoff Indices for Circulant Graphs”, Sib Math J, 65:6 (2024), 1359  crossref
    4. A. D. Mednykh, I. A. Mednykh, “Cyclic coverings of graphs. Counting rooted spanning forests and trees, Kirchhoff index, and Jacobians”, Russian Math. Surveys, 78:3 (2023), 501–548  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
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