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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 3 scientific papers (total in 3 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 (3)
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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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\transl
\jour Dokl. Math.
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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