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

TL;DR

This paper derives explicit formulas for the Kirchhoff and degree-Kirchhoff indices of linear crossed octagonal-quadrilateral networks, revealing their proportionality to Wiener and Gutman indices, respectively.

Contribution

It provides closed-form formulas for these indices and the number of spanning trees, extending prior work on similar network structures.

Findings

Formulas for Kirchhoff index and degree-Kirchhoff index of $Q_n$

Relation between Kirchhoff indices and Wiener/Gutman indices

Explicit count of spanning trees in $Q_n$

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).