TY - JOUR
T1 - Laplacian state transfer in Q-graph
AU - Li, Yipeng
AU - Liu, Xiaogang
AU - Zhang, Shenggui
N1 - Publisher Copyright:
© 2020
PY - 2020/11/1
Y1 - 2020/11/1
N2 - The Q-graph of a graph G is defined to be the graph obtained from G by inserting a new vertex into each edge of G, and joining by edges those pairs of new vertices which lie on adjacent edges of G. In this paper, we investigate the existence of Laplacian perfect state transfer and Laplacian pretty good state transfer in Q-graphs of r-regular graphs for r ≥ 2. We prove that there is no Laplacian perfect state transfer in the Q-graph of an r-regular graph, if r+1 is a prime number. In contrast, we give sufficient conditions for the Q-graph of an r-regular graph, where r+1 is a prime number, to have Laplacian pretty good state transfer.
AB - The Q-graph of a graph G is defined to be the graph obtained from G by inserting a new vertex into each edge of G, and joining by edges those pairs of new vertices which lie on adjacent edges of G. In this paper, we investigate the existence of Laplacian perfect state transfer and Laplacian pretty good state transfer in Q-graphs of r-regular graphs for r ≥ 2. We prove that there is no Laplacian perfect state transfer in the Q-graph of an r-regular graph, if r+1 is a prime number. In contrast, we give sufficient conditions for the Q-graph of an r-regular graph, where r+1 is a prime number, to have Laplacian pretty good state transfer.
KW - Continuous-time quantum walk
KW - Laplacian perfect state transfer
KW - Laplacian pretty good state transfer
KW - Q-graph
UR - https://www.scopus.com/pages/publications/85085273939
U2 - 10.1016/j.amc.2020.125370
DO - 10.1016/j.amc.2020.125370
M3 - 文章
AN - SCOPUS:85085273939
SN - 0096-3003
VL - 384
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
M1 - 125370
ER -