Kirchhoff Index for Circulant Graphs and Its Asymptotics

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The aim of this paper is to find an analytical formula for the Kirchhoff index of circulant graphs (Formula presented.) with even and odd valency, respectively. The asymptotic behavior of the Kirchhoff index as n → ∞ 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 → ∞.

Original languageEnglish
Pages (from-to)392-395
Number of pages4
JournalDoklady Mathematics
Issue number2
Publication statusPublished - Sep 2020


  • : circulant graph
  • eigenvalue
  • Kirchhoff index
  • Laplacian matrix
  • Wiener index
  • circulant graph

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