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Sibirskii Matematicheskii Zhurnal, 2024, Volume 65, Number 6, Pages 1191–1206
DOI: https://doi.org/10.33048/smzh.2024.65.610 (Mi smj7918) 		 
This article is cited in 1 scientific paper (total in 1 paper)

The Kirchhoff indices for circulant graphs

A. D. Mednykhab, I. A. Mednykhab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/smzh.2024.65.610
Abstract: We present an approach yielding closed analytical formulas for the Kirchhoff indices of circulant graphs with even and odd vertex valency respectively and the prism-like graphs based on circulant graphs. Inspecting the asymptotics of the Kirchhoff index we show that in each of the above-mentioned cases the index can be expressed as the sum of a cubic polynomial and an exponentially vanishing remainder term.
Keywords: circulant graph, Laplace matrix, eigenvalue, Wiener index, Kirchhoff index.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation FWNF-2022-0005
The work was carried out in the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF–2022–0005).
Received: 28.08.2024
Revised: 28.08.2024
Accepted: 23.10.2024
English version:
Siberian Mathematical Journal, 2024, Volume 65, Issue 6, Pages 1359–1372
DOI: https://doi.org/10.1134/S0037446624060107
Document Type: Article
UDC: 517.545+517.962.2+519.173
MSC: 35R30
Language: Russian
Citation: A. D. Mednykh, I. A. Mednykh, “The Kirchhoff indices for circulant graphs”, Sibirsk. Mat. Zh., 65:6 (2024), 1191–1206; Siberian Math. J., 65:6 (2024), 1359–1372
Citation in format AMSBIB
\Bibitem{MedMed24}
\by A.~D.~Mednykh, I.~A.~Mednykh
\paper The Kirchhoff indices for circulant graphs
\jour Sibirsk. Mat. Zh.
\yr 2024
\vol 65
\issue 6
\pages 1191--1206
\mathnet{http://mi.mathnet.ru/smj7918}
\transl
\jour Siberian Math. J.
\yr 2024
\vol 65
\issue 6
\pages 1359--1372
\crossref{https://doi.org/10.1134/S0037446624060107}
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