剖分图上的无符号拉普拉斯完美态转移  

Signless Laplacian perfect state transfer in subdivision graph

作　　者：康春辉 KANG Chunhui(Department of Mathematics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《哈尔滨商业大学学报（自然科学版）》2024年第4期449-454,共6页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：国家自然科学基金(No.11561040);甘肃省自然科学基金(No.20JR5RA418)。

摘　　要：图G的剖分图S(G)是通过在图G的每条边中插入一个新的顶点而得到的图.为解决剖分图的无符号拉普拉斯完美态转移问题,采用剖分图的无符号拉普拉斯矩阵的谱分解形式,对r-正则图G(r≥2)的剖分图S(G)上的无符号拉普拉斯完美态转移问题进行研究,得到了r-正则图G(r≥2)的剖分图S(G)的特征值和对应的特征投影,结果表明,若r-1不是图G的无符号拉普拉斯特征值,则S(G)不存在无符号拉普拉斯完美态转移.The subdivision graph S(G)of a graph is a graph obtained by inserting a new vertex into each edge of G.In order to solve the problem of perfect state subdivision graph.Using the spectral decomposition form of signless Laplacian matrix of subdivision graph,this paper investigated the existence of signless Laplacian perfect state transfer in the subdivision graph S(G)of an r-regular graph,where r≥2.Obtained the signless Laplacian eigenvalues and corresponding eigenprojections for subdivision graphs of regular graphs,the results showed that if r-1 was not signles Laplacian eigenvalue of an graph G,then there was no signless Laplacian perfect state transfer in S(G).

关 键 词：剖分图 特征值 特征向量 谱分解 完美态转移 

分 类 号：O157.5[理学—数学]