具有固定控制数的树的调和指数

doi:10.15960/j.cnki.issn.1007-6093.2025.01.017

运筹学学报（中英文） ›› 2025, Vol. 29 ›› Issue (1): 207-215.doi: 10.15960/j.cnki.issn.1007-6093.2025.01.017

具有固定控制数的树的调和指数

孙晓玲¹^,*(), 高玉斌¹, 杜建伟¹

1. 中北大学数学学院, 山西太原 030051

收稿日期:2021-09-08 出版日期:2025-03-15 发布日期:2025-03-08
通讯作者: 孙晓玲 E-mail:sunxiaoling@nuc.edu.cn
基金资助:
山西省自然科学基金(202303021211154)

On harmonic index of trees with fixed domination number

Xiaoling SUN¹^,*(), Yubin GAO¹, Jianwei DU¹

1. School of Mathematics, North University of China, Taiyuan 030051, Shanxi, China

Received:2021-09-08 Online:2025-03-15 Published:2025-03-08
Contact: Xiaoling SUN E-mail:sunxiaoling@nuc.edu.cn

摘要/Abstract

摘要：

为了预测分子的物理、化学性质和生物活性, 科学家们提出了许多拓扑指数。调和指数是著名的Randić指数的一种变形形式, 研究表明该指数能有效地预测化合物的物理化学性质。对具有固定控制数的树的调和指数进行了研究, 通过分析具有固定控制数的树的结构, 利用数学归纳法, 给出了具有固定控制数的树的调和指数的最大值和最小值, 并刻画了达到最值的树。

关键词: 调和指数, 树, 控制数

Abstract:

In order to predict the physical, chemical properties and biological activities of molecules, scientists have proposed many topological indices. As a variant of the well known Randićindex, the harmonic index is proven to be a valuable predictive index in the study of the physical and chemical properties of compounds. The harmonic index of trees with fixed domination number was investigated. By analyzing the structure of trees with fixed domination number and using the method of mathematical induction, the maximum and minimum harmonic indices of trees with fixed domination number are presented. Furthermore, the corresponding extremal trees are determined.

Key words: harmonic index, tree, domination number

中图分类号:

O157.5

孙晓玲, 高玉斌, 杜建伟. 具有固定控制数的树的调和指数[J]. 运筹学学报（中英文）, 2025, 29(1): 207-215.

Xiaoling SUN, Yubin GAO, Jianwei DU. On harmonic index of trees with fixed domination number[J]. Operations Research Transactions, 2025, 29(1): 207-215.

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具有固定控制数的树的调和指数

On harmonic index of trees with fixed domination number

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