图的支配 Hyper Zagreb 指数问题研究

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文章编号：1003-6180（2026）02-0007-06

[中图分类号]O157.5 [文献标志码]A

Research on the Problem of the Dominating Hyper Zagreb Index of Graphs

CHEN Zhuangzhuang， GENG Xianya*

（School of Mathematics and Big Data， Anhui University of Science and Technology， Huainan ， China）

Abstract： In order to convert the structure of compounds into mathematical objects， researchers use various topological indices to quantify the structural characteristics of graphs. Among them， the dominating Hyper Zagreb index is an emerging dominating topological index in recent years， which can effectively reveal the structural characteristics of compounds. At present， the research on the extreme values of this index has been carried out for graphs， trees， and wheel graphs with fixed orders. This paper calculates the dominating Hyper Zagreb index and the modified dominating Hyper Zagreb index of some special graphs， namely windmill graphs and book graphs， and also explores other properties of this index.

Keywords： dominating Hyper Zagreb index; special graphs; windmill graphs; book graphs

拓扑指数在化学图论和网络科学中具有广泛应用，研究人员借助各种拓扑指数来量化图的结构特性，目的是将化合物结构转化为数学对象．Hyper Zagreb 指数是图论中一个重要的指数，最早由 SHIRDEL [3] 等人在 2013 年提出．支配 Hyper Zagreb 指数能有效揭示化合物的结构特性．目前已针对固定阶数的图、树、轮图开展其指数极值研究，其定义为：

学者就此问题在图论和化学图论等领域展开研究 [4] ，并研究了图的四种运算的 Hyper Zagreb 指数。（剩余4271字）