图的电阻距离综述  

A Survey on Resistance Distance of Graph

作　　者：杨玉军 YANG Yujun(School of Mathematics and Information Sciences,Yantai University,Yantai 264005,China)

机构地区：[1]烟台大学数学与信息科学学院,山东烟台264005

出　　处：《集美大学学报（自然科学版）》2022年第1期1-16,共16页Journal of Jimei University：Natural Science

基　　金：国家自然科学基金项目(11671347,12171414);山东省自然科学基金项目(ZR2019YQ02)。

摘　　要：设G是连通图,G中任意两点之间的电阻距离定义为将G中的每条边用电阻(通常用单位电阻)代替后所得到的电网络中这两个节点之间的等效电阻。综述了电阻距离领域的研究进展和重要研究成果,包括电阻距离的计算公式、电阻距离的性质、电阻距离的和法则、电阻距离的递推公式以及若干重要图类的电阻距离解析计算公式。最后,给出了电阻距离研究领域的一个公开问题和两个猜想。Let G be a connected graph.The resistance distance between any two vertices of G is defined as the effective resistance between them in the electrical network constructed from G by replacing each edge of G with a resistor(usually by a unit resistor).In the present work,research progress and important research results on resistance distance were surveied,including formulas for computing resistance distance,properties on resistance distance,sum rules on resistance distance,a recursion formula on resistance distance,and analytical formula for resistance distance of some important classes of graphs.Finally,an open problem and two conjectures on resistance distance were proposed.

关 键 词：电阻距离 LAPLACIAN矩阵 图上随机游走 Rayleigh单调性法则 生成树 

分 类 号：O157.5[理学—数学]