The (degree)-Kirchhoff index of linear crossed octagonal-quadrilateral networks

2022/06/19 by Jia‐Bao Liu, Ting Zhang, Liu, Jia-Bao +3
Chemistry · Computer Science · Mathematics · #Combinatorics (math.CO) #Computational Drug Discovery Methods #FOS: Mathematics #Graph theory and applications #Molecular spectroscopy and chirality #Spectral Theory (math.SP)

paper · pdf · doi:10.48550/arxiv.2206.09447

openalex publication_date 2022/06/19 · openalex created_date 2022/06/24 · openalex updated_date 2026/07/28

Abstract

The Kirchhoff index and degree-Kirchhoff index have attracted extensive attentions due to its practical applications in complex networks, physics, and chemistry. In 2019, Liu et al. [Int. J. Quantum Chem. 119 (2019) e25971] derived the formula of the degree-Kirchhoff index of linear octagonal-quadrilateral networks. In the present paper, we consider linear crossed octagonal-quadrilateral networks Q_n. Explicit closed-form formulas of the Kirchhoff index, the degree-Kirchhoff index, and the number of spanning trees of Q_n are obtained. Moreover, the Kirchhoff index (resp. degree-Kirchhoff index) of Q_n is shown to be almost 1/4 of its Wiener index (resp. Gutman index).

Related

• Kirchhoff index, multiplicative degree-Kirchhoff index and spanning trees of the linear crossed polyomino chains
• The Laplacians, Kirchhoff index and complexity of linear Möbius and cylinder octagonal-quadrilateral networks
• Resistance distance-based graph invariants and the number of spanning trees of linear crossed octagonal graphs
• Extremal Kirchhoff index in polycyclic chains
• Computing the Laplacian spectrum of linear octagonal-quadrilateral networks and its applications