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Kirchhoff index of a linear hexagonal chain

zhenzhen Lou

University of Shanghai for Science and Technology

Author Profile## Abstract

Let $H_n$ be a linear hexagonal chain with $n$ hexagons. In this
paper, we give a decomposition theorem of Laplacian polynomial of
weighted graphs and obtain that the Laplacian spectrum of $H_n$
consists of the eigenvalues of a symmetric tridiagonal matrices of order
$4n+2$ and the Laplacian eigenvalues of $2n$ $K_2s$. Together
with the relationship between the roots and coefficients of the
characteristic polynomials of the above matrices, explicit formula of
the Kirchhoff index of $H_n$ is derived. We also give the number of
spanning trees of $H_n$, and show that the Kirchhoff index of
$H_n$ is approximately one half of its Wiener index.