摘要
该文利用群的表示和特征标研究了双循环群T_(4n)=〈a,b|a^(2n)=1,a^(n)=b^(2),b^(-1)ab=a^(-1)〉上凯莱图Cay(T_(4n),S)的完美边态转移.对T_(4n)的对称子集S,当n为奇数时,证明了图Cay(T_(4n),S)中任意两条边之间不存在完美边态转移;当n为偶数时,刻画了Cay(T_(4n),S)存在完美边态转移的条件.
In this paper,the perfect edge state transfe on Cayley graph over the dicyclc group T_(4n)=〈a,b|a^(2n)=1,a^(n)=b^(2),b^(-1)ab=a^(-1)〉is studied by the representation and character theory of a group.For a symmetric subset S of T_(4n),it is proved that perfect edge state transfer between any two edges of Cayley graph Cay(T_(4n),S)does not exist when n is odd,and the conditions for the existence of perfect edge state transfer on the graph are characterized when n is even.
作者
陶亚雯
王维忠
TAO Yawen;WANG Weizhong(Department of Mathematics,Lanzhou Jiaotong University,Lanzhou 730070,China)
出处
《华中师范大学学报(自然科学版)》
北大核心
2025年第4期561-567,共7页
Journal of Central China Normal University:Natural Sciences
基金
国家自然科学基金项目(11961040)
甘肃省自然科学基金项目(20JR5RA418).
关键词
凯莱图
双循环群
完美边态转移
量子行走
Cayley graphs
dicyclic groups
perfect edge state transfer
quantum random walk
