Laplacian state transfer in edge coronas

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.