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Laplacian State Transfer in Coronas | | Ethan Ackelsberg
; Zachary Brehm
; Ada Chan
; Joshua Mundinger
; Christino Tamon
; | | Date: |
22 Aug 2015 | | Abstract: | 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 of 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. | | Source: | arXiv, 1508.5458 | | Services: | Forum | Review | PDF | Favorites | |
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