The signless Laplacian state transfer in coronas.

For two graphs G and H, the corona product G ∘ H is the graph obtained by taking one copy of G and | V G | copies of H, and joining the ith vertex of G with every vertex of the ith copy of H. In this paper, we study the state transfer of corona relative to the signless Laplacian matrix. We explore some conditions that guarantee the signless Laplacian perfect state transfer in G ∘ H . We prove that G ∘ K m has no signless Laplacian perfect state transfer for some special m. We also show that K 2 ∘ H has pretty good state transfer but no perfect state transfer relative to the signless Laplacian matrix for a regular graph H. Furthermore, we show that n K 2 ¯ ∘ K 1 has signless Laplacian pretty good state transfer, where n K 2 ¯ is the cocktail party graph. [ABSTRACT FROM AUTHOR]