单圈图的Steiner k-Wiener指标的下界  

The Lower Bound of the Steiner k-Wiener Index of Unicyclic Graphs

作　　者：王鹏飞[1] 殷凤[1] 王朝平 何瑞强[1] WANG Pengfei;YIN Feng;WANG Chaoping;HE Ruiqiang(Department of Mathematics,Xinzhou Normal University,Xinzhou 034000,China;School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730030,China)

机构地区：[1]忻州师范学院数学系,山西忻州034000 [2]兰州交通大学数理学院,甘肃兰州730030

出　　处：《山西大学学报（自然科学版）》2024年第6期1155-1163,共9页Journal of Shanxi University(Natural Science Edition)

基　　金：山西省基础研究计划(202303021221175)。

摘　　要：为了发展并完善图论中拓扑指标的基本理论,本文利用图形变换的方法确定了单圈图Steiner k-Wiener指标的下界,并刻画了达到下界时的极图。首先,通过研究单圈图的结构对Steiner k-Wiener指标的影响,确定了一系列使该指标减小的图形变换。进而找到了不同条件下最小Steiner k-Wiener指标所对应的极值图。最后,得到了上述极值图所对应的Steiner k-Wiener指标数值。基于此,本文推广并完善了单圈图Steiner k-Wiener指标下界问题的研究成果,丰富了拓扑指标问题的研究内容,为图论中拓扑指标问题在数学以及化学领域的广泛应用提供了理论依据。In order to develop and perfect the basic theory of topological index in graph theory, a lower bound of the Steiner k-Wiener index of unicyclic graphs is determined by the method of graph transformation, and the extremal graphs are described when the lower bound is reached. Firstly, by studying the influence of the structure of unicyclic graphs on the Steiner k-Wiener index, a series of graph transformations are determined to reduce the index. Then, the extremal graphs corresponding to the minimum Steiner kWiener index under different conditions are obtained. Finally, the Steiner k-Wiener index values corresponding to the above the extremal graphs are presented. Based on this, this paper extends and improves the research results of the Steiner k-Wiener index lower bound problem of unicyclic graphs, enriches the research content of topological index problem, and provides a theoretical basis for the wide application of topological index problem of graph theory in mathematics and chemistry.

关 键 词：单圈图 Steiner k-Wiener指标 Steiner距离 

分 类 号：O157.5[理学—数学]