一般图与二部图中完美匹配关于距离无符号拉普拉斯谱半径的存在性  

Existence of Perfect Matchings in General Graphs and Bipartite Graphs with Respect to Distance Signless Laplacian Spectral Radius

作　　者：严子墨 刘畅 李建平[1] Yan Zimo;Liu Chang;Li Jianping(College of Sciences,National University of Defense Technology,Changsha 410073,China)

机构地区：[1]国防科技大学理学院,长沙410073

出　　处：《数学理论与应用》2023年第1期74-84,共11页Mathematical Theory and Applications

基　　金：National Natural Science Foundation of China(No.61773020)。

摘　　要：令D(G)=(D_(i,j))为连通图G的距离矩阵,其中D_(i,j)等于顶点v_(i)和v_(j)之间的距离.令η1(G)为图G的距离无符号拉普拉斯谱半径,即距离无符号拉普拉斯矩阵Q(G)=Diag(Tr)+D(G)的最大特征值,其中Diag(Tr)为对角矩阵,Diag(Tr)_(ii)=Σ_(vivj∈E)(G)D_(i,j).在本文中,我们研究图中完美匹配的存在性与距离无符号拉普拉斯谱半径之间的关系,并分别给出关于距离无符号拉普拉斯谱半径的一般图和二部图存在完美匹配的充分条件.LetD(G)=(D_(i,j))be the distance matrix of a connected graphG,whereD_(i,j)equals the distance between the vertices v_(i) and v_(j) ofG.Letη1(G)be the distance signless Laplacian spectral radius ofG,i.e.,the largest eigenvalue of the distance signless Laplacian matrix Q(G)=Diag(Tr)+D(G),where Diag(Tr)is a diagonal matrix with Diag(Tr)_(ii)=Σ_(vivj∈E)(G)D_(i,j).In this paper,we investigate the relationships between the perfect matchings and the distance signless Laplacian spectral radius,and give sufficient conditions for the existence of perfect matchings in general graphs and bipartite graphs with respect to the distance signless Laplacian spectral radius,respectively.

关 键 词：距离无符号拉普拉斯谱半径 完美匹配 二部图 

分 类 号：O157.5[理学—数学]