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arXiv · 2009.04621

The Laplacian spectrum, Kirchhoff index and complexity of the linear heptagonal networks

Jia-Bao Liu·Jing Chen·Jing Zhao·Shaohui Wang
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Abstract

Let $H_n$ be the linear heptagonal networks with $2n$ heptagons. We study the structure properties and the eigenvalues of the linear heptagonal networks. According to the Laplacian polynomial of $H_n$, we utilize the decomposition theorem. Thus, the Laplacian spectrum of $H_n$ is created by eigenvalues of a pair of matrices: $L_A$ and $L_S$ of order number $5n+1$ and $4n+1$, respectively. On the basis of the roots and coefficients of their characteristic polynomials of $L_A$ and $L_S$, we not only get the explicit forms of Kirchhoff index, but also corresponding total complexity of $H_n$.

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Jia-Bao Liu, Jing Chen, Jing Zhao, Shaohui Wang. 2020-09-10. The Laplacian spectrum, Kirchhoff index and complexity of the linear heptagonal networks. https://arxiv.org/abs/2009.04621

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