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Research Article | Open Access

Degree-weighted Wiener index of a graph

Zhen Lin1( ), Ting Zhou2
School of Mathematics and Statistics, Qinghai Normal University, Xi'ning 810008, China
School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China
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Abstract

From geometric point of view, we introduced the Sombor-Wiener index of a graph and studied the basic properties of the new index. It was shown that the Sombor-Wiener index was useful in predicting the acentric factor of octane isomers. In addition, we proposed a degree-weighted Wiener index to generalize the Schultz index, the Gutman index, and the Sombor-Wiener index. Meanwhile, we gave the calculation formula of degree-weighted Wiener index for generalized Bethe trees.

Keywords

Sombor-Wiener indexdegree-weighted Wiener indextree

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Mathematical Modelling and Control
Volume 4 Issue 1,
April 2024
Pages 9-16
DOI: 10.3934/mmc.2024002

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Cite this article:
Lin Z, Zhou T. Degree-weighted Wiener index of a graph. Mathematical Modelling and Control, 2024, 4(1): 9-16. https://doi.org/10.3934/mmc.2024002

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Received: 11 May 2023
Revised: 05 December 2023
Accepted: 15 December 2023
Published: 14 March 2024
©2024 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)