拓展邻冠的完美态传递
Perfect State Transfer on Extended Neighborhood Corona Graphs
DOI: 10.12677/AAM.2026.154179, PDF,   
作者: 戴高乐：浙江师范大学数学科学学院，浙江 金华
关键词: 完美态传递；邻接矩阵；拓展邻冠图；Perfect State Transfer； Adjacency Matrix； Extended Neighborhood Corona Graph
摘要: 本文研究拓展邻冠图上的完美态传递问题。 针对拓展邻冠图的构造，我们给出一个有关图参数的 充分条件使得拓展邻冠图G ∗ H 上不存在完美态传递。通过具体实例，我们验证了这一条件的有效 性，并展示了不存在完美态传递的图类。 该结果为量子网络中基于冠图结构的节点间态传输可行 性提供了理论判据。
Abstract: This paper investigates the problem of perfect state transfer on extended neighborhood corona graphs. For the construction of extended neighborhood corona graphs, we present a sufficient condition related to graph parameters such that there is no perfect state transfer on the extended neighborhood corona graph G ∗ H. Through concrete examples, we verify the validity of this condition and demonstrate classes of graphs that do not admit perfect state transfer. This result provides a theoretical criterion for the feasibility of state transfer between nodes in quantum networks based on corona graph structures.
文章引用：戴高乐. 拓展邻冠的完美态传递[J]. 应用数学进展, 2026, 15(4): 519-527. https://doi.org/10.12677/AAM.2026.154179

参考文献

[1] Farhi, E. and Gutmann, S. (1998) Quantum Computation and Decision Trees. Physical Review A, 58, 915-928. [Google Scholar] [CrossRef] 
[2] Christandl, M., Datta, N., Ekert, A. and Landahl, A.J. (2004) Perfect State Transfer in Quan- tum Spin Networks. Physical Review Letters, 92, Article 187902. [Google Scholar] [CrossRef] 
[3] Godsil, C. (2012) When Can Perfect State Transfer Occur? The Electronic Journal of Linear Algebra, 23, 877-890. [Google Scholar] [CrossRef] 
[4] Godsil, C. (2012) State Transfer on Graphs. Discrete Mathematics, 312, 129-147. [Google Scholar] [CrossRef] 
[5] Ackelsberg, E., Brehm, Z., Chan, A., Mundinger, J. and Tamon, C. (2017) Quantum State Transfer in Coronas. The Electronic Journal of Combinatorics, 24, P2.24. [Google Scholar] [CrossRef] 
[6] Zhang, X., Xiong, Q., Tian, G. and Cui, S. (2023) Quantum State Transfer on Neighborhood Corona of Two Graphs. Bulletin of the Malaysian Mathematical Sciences Society, 46, Article No. 11. [Google Scholar] [CrossRef] 
[7] Wang, J. and Liu, X. (2022) State Transfers in Vertex Complemented Coronas. Discrete Applied Mathematics, 321, 165-178. [Google Scholar] [CrossRef] 
[8] Li, Y., Liu, X. and Zhang, S. (2020) Laplacian State Transfer in Edge Coronas. Linear and Multilinear Algebra, 70, 1023-1046. [Google Scholar] [CrossRef] 
[9] Li, Y.P., Liu, X.G. and Zhang, S.G. (2021) Laplacian Perfect State Transfer in Extended Neighborhood Coronas. Acta Mathematica Sinica, English Series, 37, 1921-1932. [Google Scholar] [CrossRef] 
[10] Coutinho, G. (2014) Quantum State Transfer in Graphs. PhD Thesis, University of Waterloo.
[11] Adiga, C., Rakshith, B.R. and Krishna, K.N.S. (2016) Spectra of the Extended Neighbor- hood Corona and Extended Corona of Two Graphs. Electronic Journal of Graph Theory and Applications, 4, 101-110. [Google Scholar] [CrossRef] 

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