剖分图上的完美态传递  

Perfect State Transfer in Subdivision Graph

作　　者：康春辉 KANG Chun-hui(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou Gansu 730070,China)

机构地区：[1]兰州交通大学数理学院,甘肃兰州730070

出　　处：《淮阴师范学院学报（自然科学版）》2024年第3期205-209,共5页Journal of Huaiyin Teachers College(Natural Science Edition)

基　　金：甘肃省自然科学基金(11561042)。

摘　　要：研究了r-正则图G(r≥2)的剖分图S(G)上的完美态传递问题,并证明了当λ_(s)+r(0≤s≤d)是一个非完全平方数时,则S(G)的任意两个顶点之间不存在完美态传递.Let G a simple undirected and connected r-regular graph of n order,λ_(0)>λ_(1)>…>λ_(d) is all the distinct eigenvalues of its adjacency matrix.The subdivision graph S(G)of a graph G is a graph obtained by inserting a new vertex into each edge of G.In this paper,we investigate the existence of perfect state transfer in the subdivision graph S(G)of an r-regular graph,where r≥2.It is proved that if λ_(s)+r(0≤s≤d)is a square-free integers,then there is no perfect state transfer between any two vertices in S(G).

关 键 词：剖分图 特征值 完美态传递 

分 类 号：O157.5[理学—数学]