The Laplacians, Kirchhoff index and complexity of linear Möbius and cylinder octagonal-quadrilateral networks

2022/05/02 by Liu, Jia-Bao, Fang, Lu-Lu, Zheng, Qian +1
#Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2205.00866

Abstract

Spectrum graph theory not only facilitate comprehensively reflect the topological structure and dynamic characteristics of networks, but also offer significant and noteworthy applications in theoretical chemistry, network science and other fields. Let L_n^8,4 represent a linear octagonal-quadrilateral network, consisting of n eight-member ring and n four-member ring. The Möbius graph Q_n(8,4) is constructed by reverse identifying the opposite edges, whereas cylinder graph Q'_n(8,4) identifies the opposite edges by order. In this paper, the explicit formulas of Kirchhoff indices and complexity of Q_n(8,4) and Q'_n(8,4) are demonstrated by Laplacian characteristic polynomials according to decomposition theorem and Vieta's theorem. In surprise, the Kirchhoff index of Q_n(8,4)(Q'_n(8,4)) is approximately one-third half of its Wiener index as n→∞.

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