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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2019, Volume 16, Pages 1654–1661
DOI: https://doi.org/10.33048/semi.2019.16.117
(Mi semr1158)
 

This article is cited in 2 scientific papers (total in 2 papers)

Discrete mathematics and mathematical cybernetics

Elementary formulas for Kirchhoff index of Möbius ladder and Prism graphs

G. A. Baigonakovaa, A. D. Mednykhbc

a Gorno-Altaysk State University, 34, Socialisticheskaya str., Gorno-Altaysk, 639000, Russia
b Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
c Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
Full-text PDF (152 kB) Citations (2)
References:
Abstract: Let $G$ be a finite connected graph on $n$ vertices with Laplacian spectrum $0=\lambda_1<\lambda_2\le\ldots\le\lambda_n.$ The Kirchhoff index of $G$ is defined by the formula
$$Kf(G)=n\sum\limits_{j=2}^n\frac{1}{\lambda_j}.$$
The aim of this paper is to find an explicit analytical formula for the Kirchhoff index of Möbius ladder graph $M_n=C_{2n}(1,n)$ and Prism graph $Pr_n=C_n\times P_2$. The obtained formulas provide a simple asymptotical behavior of both invariants as $n$ is going to the infinity.
Keywords: Laplacian matrix, circulant graph, Kirchhoff index, Wiener index, Chebyshev polynomial.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00420_а
18-501-51021_НИФ_а
This work was partially supported by the Russian Foundation for Basic Research (projects 18-01-00420 and 18-501-51021).
Received March 15, 2019, published November 21, 2019
Bibliographic databases:
Document Type: Article
UDC: 519.175.3, 519.172
MSC: 05C30, 39A10
Language: English
Citation: G. A. Baigonakova, A. D. Mednykh, “Elementary formulas for Kirchhoff index of Möbius ladder and Prism graphs”, Sib. Èlektron. Mat. Izv., 16 (2019), 1654–1661
Citation in format AMSBIB
\Bibitem{BaiMed19}
\by G.~A.~Baigonakova, A.~D.~Mednykh
\paper Elementary formulas for Kirchhoff index of M\"obius ladder and Prism graphs
\jour Sib. \`Elektron. Mat. Izv.
\yr 2019
\vol 16
\pages 1654--1661
\mathnet{http://mi.mathnet.ru/semr1158}
\crossref{https://doi.org/10.33048/semi.2019.16.117}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000497717700001}
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  • https://www.mathnet.ru/eng/semr/v16/p1654
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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