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

2020/09/10 by Jia-Bao Liu, Jing Chen, Liu, Jia-Bao +5
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Spectral Theory (math.SP) #math.CO #math.SP

paper · pdf · doi:10.48550/arxiv.2009.04621

arxiv created 2020/09/10 · arxiv updated 2020/09/11

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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