Laplacian state transfer in total graphs

Laplacian state transfer in vertex complemented coronas

“…• If r + 1 is not a Laplacian eigenvalue of an r-regular graph G, then there is no LPST in the total graph of G, but it has LPGST under some mild conditions [32].…”

Constructing graphs having Laplacian pair state transfer by an edge perturbation

“…where γ is a complex scalar and |γ| = 1, which is equivalent to Pair state transfers can be regarded as generalizations of state transfers, which are very important in quantum computing and quantum information processing [12,20,21]. Up until now, many graphs have been shown to admit state transfers, including trees [4,14,16,19], Cayley graphs [3, 6-8, 11, 26, 29-32], distance regular graphs [13] and some graph operations such as NEPS [22,25,27,34], coronas [1,2], edge complemented coronas [33] and total graphs [23]. For more information, we refer the reader to [15,17,18,35,36].…”

Quantum State Transfer on Neighborhood Corona of Two Graphs

“…Recently, Li et al [17] gave some sufficient conditions for extended neighborhood coronas to have Laplacian perfect state transfer. For more details about these directions, readers may refer to [3,7,8,9,19,24].…”