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Laplacian state transfer in coronas

2016; Elsevier BV; Volume: 506; Linguagem: Inglês

10.1016/j.laa.2016.05.018

1873-1856

Ethan Ackelsberg, Zachary Brehm, Ada Chan, Joshua Mundinger, Christino Tamon,

Advanced Memory and Neural Computing

We prove that the corona product of two graphs has no Laplacian perfect state transfer whenever the first graph has at least two vertices. This complements a result of Coutinho and Liu who showed that no tree of size greater than two has Laplacian perfect state transfer. In contrast, we prove that the corona product of two graphs exhibits Laplacian pretty good state transfer, under some mild conditions. This provides the first known examples of families of graphs with Laplacian pretty good state transfer. Our result extends the work of Fan and Godsil on double stars to the Laplacian setting. Moreover, we also show that the corona product of any cocktail party graph with a single vertex graph has Laplacian pretty good state transfer, even though odd cocktail party graphs have no perfect state transfer.