ABSTRACT

Characterizing which graphs have Laplaican perfect state transfer or Laplacian pretty good state transfer is an interesting and desirable problem. In this paper, we investigate the existence of Laplacian perfect state transfer and Laplacian pretty good state transfer in edge coronas. We give sufficient conditions for edge coronas to not have Laplacian perfect state transfer as well as sufficient conditions for edge coronas to have Laplacian perfect state transfer. Additionally, we also give sufficient conditions for edge coronas to have Laplacian pretty good state transfer.

中文翻译：

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边缘电晕中的拉普拉斯状态转移

摘要

表征哪些图具有拉普拉斯完美状态转移或拉普拉斯相当好的状态转移是一个有趣且理想的问题。在本文中，我们研究了边缘电晕中拉普拉斯完美状态转移和拉普拉斯相当好的状态转移的存在。我们给出了边缘电晕不具有拉普拉斯完美状态转移的充分条件，以及边缘电晕具有拉普拉斯完美状态转移的充分条件。此外，我们还为边缘电晕具有拉普拉斯相当好的状态转移提供了充分的条件。