Cayley graphs of dihedral groups having perfect edge state transfer

被引：6

作者：

Luo, Gaojun ^{[1
]}

Cao, Xiwang ^{[1
,2
]}

Xu, Guangkui ^{[3
]}

Cheng, Yingjie ^{[1
]}

机构：

[1] Nanjing Univ Aeronaut & Astronaut, Dept Math, Nanjing, Peoples R China

[2] Chinese Acad Sci, Inst Informat Engn, State Key Lab Informat Secur, Beijing, Peoples R China

[3] Huainan Normal Univ, Dept Appl Math, Huainan, Peoples R China

来源：

LINEAR & MULTILINEAR ALGEBRA | 2022年 / 70卷 / 20期

基金：

中国国家自然科学基金;

关键词：

Edge state transfer; Cayley graphs; dihedral group; spectrum;

D O I：

10.1080/03081087.2021.1940806

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Perfect state transfer plays a crucial role in quantum information processing and quantum computation. However, perfect state transfer is a rare phenomenon. As a generalization of perfect state transfer, perfect edge state transfer overcomes this disadvantage and there are more graphs admitting perfect edge state transfer than admitting perfect state transfer. In this paper, we reveal the relations between perfect state transfer and perfect edge state transfer on Cayley graphs. Furthermore, we present necessary and sufficient conditions for the existence of perfect edge state transfer on Cayley graphs of dihedral groups. With these conditions, several concrete constructions of Cayley graphs admitting perfect edge state transfer are proposed. Notably, this is the first attempt at perfect edge state transfer on Cayley graphs.

引用

页码：5957 / 5972

页数：16

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