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Laplacian state transfer in Q-graph
Applied Mathematics and Computation ( IF 3.5 ) Pub Date : 2020-11-01 , DOI: 10.1016/j.amc.2020.125370
Yipeng Li , Xiaogang Liu , Shenggui Zhang

Abstract 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.

中文翻译:

Q图中的拉普拉斯状态转移

摘要 图 G 的 Q-图被定义为通过在 G 的每条边上插入一个新顶点,并通过边连接位于 G 的相邻边上的新顶点对,从 G 获得的图。在本文中,我们研究了 r ≥ 2 的 r 正则图的 Q 图中拉普拉斯完美状态转移和拉普拉斯相当好的状态转移的存在。 我们证明了 r 正则图的 Q 图中没有拉普拉斯完美状态转移, 如果 r + 1 是素数。相比之下,我们给出了 r 正则图的 Q-图的充分条件,其中 r + 1 是素数,具有拉普拉斯非常好的状态转移。
更新日期:2020-11-01
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