Degree-weighted Wiener index of a graph

Zhen Lin; Ting Zhou; Zhen Lin; Ting Zhou

doi:10.3934/mmc.2024002

Mathematical Modelling and Control

2024, Volume 4, Issue 1: 9-16. doi: 10.3934/mmc.2024002

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Research article

Degree-weighted Wiener index of a graph

Zhen Lin ^{1
,
,},
Ting Zhou ²

1.
School of Mathematics and Statistics, Qinghai Normal University, Xi'ning 810008, China
2.
School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China

Received: 11 May 2023 Revised: 05 December 2023 Accepted: 15 December 2023 Published: 14 March 2024

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.
- Sombor-Wiener index,
- degree-weighted Wiener index,
- tree
Citation: Zhen Lin, Ting Zhou. Degree-weighted Wiener index of a graph[J]. Mathematical Modelling and Control, 2024, 4(1): 9-16. doi: 10.3934/mmc.2024002

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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.

References

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