论文标题
两个图的邻里电晕上的量子状态转移
Quantum State Transfer on Neighborhood Corona of Two Graphs
论文作者
论文摘要
给定两个图$ g_ {1} $的订单$ n_ {1} $和$ g_ {2} $，$ g_ {1} $和$ g_ {2} $的邻域电晕，由$ g_ {1} \ bigStar g_ {2} $ copy os $ g_ copper of $ g_ {1}。与此同时，在$ g_ {2} $中，链接了$ g_ {1} $的$ i $ th顶点的所有邻居，并使用$ i $ th副本的所有顶点$ g_ {2} $。在我们的工作中，我们给出了一些条件，即$ g_ {1} \ bigstar g_ {2} $不是周期性的。此外，我们为$ g_ {1} \ bigstar g_ {2} $展示了一些足够的条件，没有完美的状态转移。提供了一些示例来解释我们的结果。此外，由于公认的完美状态转移的图形很少见，我们还认为在两个图的邻里电晕上进行了很好的状态转移。我们显示了一些$ g_ {1} \ bigstar g_ {2} $的足够条件，允许很好的状态转移。
Given two graphs $G_{1}$ of order $n_{1}$ and $G_{2}$, the neighborhood corona of $G_{1}$ and $G_{2}$, denoted by $G_{1}\bigstar G_{2}$, is the graph obtained by taking one copy of $G_{1}$ and taking $n_{1}$ copies of $G_{2}$, in the meanwhile, linking all the neighbors of the $i$-th vertex of $G_{1}$ with all vertices of the $i$-th copy of $G_{2}$. In our work, we give some conditions that $G_{1}\bigstar G_{2}$ is not periodic. Furthermore, we demonstrate some sufficient conditions for $G_{1}\bigstar G_{2}$ having no perfect state transfer. Some examples are provided to explain our results. In addition, for the reason that the graph admitting perfect state transfer is rare, we also consider pretty good state transfer on neighborhood corona of two graphs. We show some sufficient conditions for $G_{1}\bigstar G_{2}$ admitting pretty good state transfer.
