Geodesic
Kirchhoff index for circulant graphs and its asymptotics
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 494 (2020), pp. 43-47 Cet article a éte moissonné depuis la source Math-Net.Ru

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The aim of this paper is to find an analytical formula for the Kirchhoff index of circulant graphs $C_n(s_1,s_2,\dots,s_k)$ and $C_{2n}(s_1,s_2,\dots,s_k,n)$ with even and odd valency, respectively. The asymptotic behavior of the Kirchhoff index as $n\to\infty$ is investigated. We proof that the Kirchhoff index of a circulant graph can be expressed as a sum of a cubic polynomial in $n$ and a quantity that vanishes exponentially as $n\to\infty$.
Mots-clés : circulant graph, Laplacian matrix
Keywords: eigenvalue, Wiener index, Kirchhoff index. 
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A. D. Mednykh; I. A. Mednykh. Kirchhoff index for circulant graphs and its asymptotics. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 494 (2020), pp. 43-47. http://geodesic.mathdoc.fr/item/DANMA_2020_494_a9/

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