On the Kirchhoff Indices and the Numbers of Spanning Trees of Two Types of Molecular Graphs

Feng, Zhimin; Huang, Sumin; Yan, Lixia

doi:10.1080/10406638.2020.1729822

Cited by 1 publication

(1 citation statement)

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“…Finally, by comparing these indices with the Wiener index and Gutman index, the researchers observed that the multiplicative degree Kirchhoff index of L n is nearly one-quarter of its Gutman Wiener index. In their work [14], Feng et al investigated the Kirchhoff index of phenylenes. In another work [15], they studied the Kirchhoff index and the number of spanning trees of linear pentagonal derivation chains.…”

Section: Introductionmentioning

confidence: 99%

Kirchhoff Index and Degree Kirchhoff Index of Tetrahedrane-Derived Compounds

Zhao

Wang

et al. 2023

Symmetry

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Tetrahedrane-derived compounds consist of n crossed quadrilaterals and possess complex three-dimensional structures with high symmetry and dense spatial arrangements. As a result, these compounds hold great potential for applications in materials science, catalytic chemistry, and other related fields. The Kirchhoff index of a graph G is defined as the sum of resistive distances between any two vertices in G. This article focuses on studying a type of tetrafunctional compound with a linear crossed square chain shape. The Kirchhoff index and degree Kirchhoff index of this compound are calculated, and a detailed analysis and discussion is conducted. The calculation formula for the Kirchhoff index is obtained based on the relationship between the Kirchhoff index and Laplace eigenvalue, and the number of spanning trees is derived for linear crossed quadrangular chains. The obtained formula is validated using Ohm’s law and Cayley’s theorem. Asymptotically, the ratio of Kirchhoff index to Wiener index approaches one-fourth. Additionally, the expression for the degree Kirchhoff index of the linear crossed quadrangular chain is obtained through the relationship between the degree Kirchhoff index and the regular Laplace eigenvalue and matrix decomposition theorem.

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Section: Introductionmentioning

confidence: 99%