论文标题
Laplacians，Kirchhoff指数以及线性Möbius和圆柱八角形官方网络的复杂性
The Laplacians, Kirchhoff index and complexity of linear Möbius and cylinder octagonal-quadrilateral networks
论文作者
论文摘要
Spectrum图理论不仅有助于全面反映网络的拓扑结构和动态特征，而且还为理论化学，网络科学和其他领域提供了重要的，值得注意的应用。令$ l_ {n}^{8,4} $代表一个线性八角形Quadrilital网络，由$ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $四成员戒指组成。 Möbius图$ q_ {n}（8,4）$是通过反向识别相反边的构建的，而圆柱图$ q'_ _ {n}（8,4）$按顺序标识了相反的边缘。在本文中，laplacian特征性的多项式根据分解theorem and vieta的理论，证明了$ q_ {n}（8,4）$和$ q'_ {n}（8,4）$的$ q_ {n}（8,4）$和$ q'_ {n}（8,4）$的复杂性的明确公式。令人惊讶的是，$ q_ {n}（8,4）$（$ q'_ {n}（8,4）$）的Kirchhoff索引约为其Wiener Index的三分之一一半，为$ n \ to \ infty $。
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 $n\to\infty$.
