图的Biharmonic指数的研究  

The Study of the Biharmonic Index of Graphs

作　　者：郑学谦 ZHENG Xueqian(Shanxi Vocational University of Engineering Science and Technology,Taiyuan 030031,China)

机构地区：[1]山西工程科技职业大学,山西太原030031

出　　处：《太原师范学院学报（自然科学版）》2022年第3期12-14,共3页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：山西大学商务学院科研基金项目(2020039).

摘　　要：图G的Biharmonic指数是图论研究中与Biharmonic距离的拓扑指数相关拓扑指标之一.图G的Biharmonic距离是2010年lipman等人提出来的,2021年,魏宇龙等人提出了图G的Biharmonic指数.本文根据图G的顶点数、边数、最大度和最小度给出了图的Biharmonic指数的上下界;利用图的Laplace特征多项式得出正则图与其线图的Biharmonic指数的关系.The Biharmonic index of a graph is one of the topological indices related to the Biharmonic distance in graph theory.The Biharmonic distance of the graph was proposed by Lipman et al in 2010,and the Biharmonic index of the graph was proposed by Wei Yulong et al in 2021.In this paper,the upper and lower bounds of the Biharmonic index of a graph are given according to the number of vertices,edges,maximum degree and minimum degree of the graph;The relation between regular graph and its Biharmonic index is obtained by using the Laplace characteristic polynomial of graph.

关 键 词：Biharmonic距离 Biharmonic指数 图的Laplace特征值 

分 类 号：O157[理学—数学]