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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
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.
Received March 15, 2019, published November 21, 2019
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
Linking options:
https://www.mathnet.ru/eng/semr1158 https://www.mathnet.ru/eng/semr/v16/p1654
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