Cayley graphs of semi-dihedral groups having perfect edge state transfer

TAO Yawen; WANG Weizhong

doi:10.13471/j.cnki.acta.snus.ZR20240238

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Cayley graphs of semi-dihedral groups having perfect edge state transfer

Research articles | 更新时间：2025-11-14

- Cayley graphs of semi-dihedral groups having perfect edge state transfer
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 64, Issue 4, Pages: 147-155(2025)
- 作者机构：
  
  兰州交通大学数理学院，甘肃兰州 730070
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.ZR20240238
  CLC： O157.5
- Received：19 July 2024，
  
  Accepted：09 October 2024，
  
  Published Online：25 July 2025，
  
  Published：25 July 2025
- 稿件说明：
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陶亚雯,王维忠.半二面体群上凯莱图的完美边态转移[J].中山大学学报(自然科学版)(中英文),2025,64(04):147-155.

TAO Yawen,WANG Weizhong.Cayley graphs of semi-dihedral groups having perfect edge state transfer[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(04):147-155.
陶亚雯,王维忠.半二面体群上凯莱图的完美边态转移[J].中山大学学报(自然科学版)(中英文),2025,64(04):147-155. DOI： 10.13471/j.cnki.acta.snus.ZR20240238.

TAO Yawen,WANG Weizhong.Cayley graphs of semi-dihedral groups having perfect edge state transfer[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2025,64(04):147-155. DOI： 10.13471/j.cnki.acta.snus.ZR20240238.

摘要

研究半二面体群

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3.72533321

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6.51933336

上凯莱图的完美边态转移. 利用

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=84832512&type=

3.72533321

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6.51933336

的表示和特征标，给出了其上凯莱图允许完美边态转移的充要条件.

Abstract

The perfect edge state transfer on Cayley graphs over semi-dihedral groups

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3.72533321

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6.51933336

is investigated. Using the representations and characters of

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， some necessary and sufficient conditions are given for admitting perfect edge state transfer of Cayley graphs over

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3.72533321

https://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=84832541&type=

6.51933336

关键词

Keywords

references

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CAO X W ， FENG K Q ， 2021 . Perfect state transfer on Cayley graphs over dihedral groups ［J］. Linear Multilinear Algebra ， 69 （ 2 ）： 343 - 360 .

CAYLEY F R S ， 1877 . On the theory of groups ［J］. Proc Lond Math Soc ， s1 - 9 （ 1 ）： 126 - 133 .

CHEN Q T ， GODSIL C ， 2019 . Edge state transfer ［EB/OL］. arXiv ： 1906 . 01591 v 1 . https：//arxiv.org/abs/1906.01591v1 https://arxiv.org/abs/1906.01591v1 .

CHEN Q T ， GODSIL C ， 2020 . Pair state transfer ［J］. Quantum Inf Process ， 19 （ 9 ）： 321 .

CHRISTANDL M ， DATTA N ， EKERT A ， et al ， 2004 . Perfect state transfer in quantum spin networks ［J］. Phys Rev Lett ， 92 （ 18 ）： 187902 .

GODSIL C ， 2011 . Periodic graphs ［J］. Electron J Combin ， 18 （ 1 ）： P23 .

GODSIL C ， 2012 . State transfer on graphs ［J］. Discrete Math ， 312 （ 1 ）： 129 - 147 .

HORMOZI M ， RODTES K ， 2013 . Symmetry classes of tensors associated with the semi-dihedral groups SD 8n ［J］. Colloq Math ， 131 （ 1 ）： 59 - 67 .

LUO G J ， CAO X W ， WANG D D ， et al ， 2022 . Perfect quantum state transfer on Cayley graphs over semi-dihedral groups ［J］. Linear Multilinear Algebra ， 70 （ 21 ）： 6358 - 6374 .

STEINBERG B ， 2011 . Representation theory of finite groups： An introductory approach ［M］. New York ： Springer .

WANG S X ， FENG T ， 2023 . Perfect state transfer on bi-Cayley graphs over abelian groups ［J］. Discrete Math ， 346 （ 6 ）： 113362 .

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