树的零度与路覆盖数的关系  

Nullity of a tree in terms of path cover number

作　　者：陈洁 王龙 CHEN Jie;WANG Long(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232000,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232000

出　　处：《哈尔滨商业大学学报（自然科学版）》2023年第4期453-455,461,共4页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：中国博士后科学基金(2019M660148)。

摘　　要：图的零度是指图G的邻接矩阵A(G)零空间的维度,亦等于其零特征值的重数,用η(G)表示.图的路覆盖是指图G中一组顶点不相交的诱导路的集合,使G的每个顶点都是其中一条路的顶点,G的路覆盖数是指G的最小路覆盖,用ρ(G)表示.2021年Wang给出了图G的零度与路覆盖数的关系:η(G)≤ρ(G),本文刻画了所有满足η(G)=ρ(G)的树.The nullity of a graph G,referred to the dimension of the zero space of the adjacency matrix A(G),which was also equal to the multiplicity of zero eigenvalues.and was expressed byη(G).The path cover of a graph referred to the set of induced paths with disjoint vertices in a graph G,such that each vertex of G was the vertex of one of the paths.And the path cover number of G referred to the minimum path cover of G,denoted byρ(G).In 2021,Wang gave the relationship between the nullity of a graph G and the number of path covers:η(G)≤ρ(G).In this paper,the trees that satisfied theη(G)=ρ(G)were characterized.

关 键 词：图 树 秩 悬挂点 路 零度 路覆盖数 

分 类 号：O157.6[理学—数学]