The signless Laplacian state transfer in coronas
Gui‐Xian Tian, Ping-Kang Yu, Shu‐Yu Cui · Linear and Multilinear Algebra · 2019
For two graphs G and H, the corona product G∘H is the graph obtained by taking one copy of G and |VG| 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∘Km has no signless Laplacian perfect state transfer for some special m. We also show that K2∘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 nK2¯∘K1 has signless Laplacian pretty good state transfer, where nK2¯ is the cocktail party graph.