Geodesic
Elementary formulas for Kirchhoff index of M\"obius ladder and Prism graphs
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1654-1661

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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: Kirchhoff index, Wiener index, Chebyshev polynomial.
Mots-clés : Laplacian matrix, circulant graph 
@article{SEMR_2019_16_a75,
     author = {G. A. Baigonakova and A. D. Mednykh},
     title = {Elementary formulas for {Kirchhoff} index of {M\"obius} ladder and {Prism} graphs},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1654--1661},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a75/}
}
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G. A. Baigonakova; A. D. Mednykh. Elementary formulas for Kirchhoff index of M\"obius ladder and Prism graphs. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 1654-1661. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a75/