Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports]
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Sib. Èlektron. Mat. Izv.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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:
PDF
HTML
DOI: https://doi.org/10.33048/semi.2019.16.117
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}
Linking options:
  • https://www.mathnet.ru/eng/semr1158
  • https://www.mathnet.ru/eng/semr/v16/p1654
    • This publication is cited in the following articles:
    1. A. D. Mednykh, I. A. Mednykh, “Kirchhoff index for circulant graphs and its asymptotics”, Dokl. Math., 102:2 (2020), 392–395  mathnet  crossref  crossref  zmath  elib
    2. 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  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Statistics & downloads:
    Abstract page:291
    Full-text PDF :168
    References:21
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024