Some classes of integral circulant graphs either allowing or not allowing perfect state transfer
Some classes of integral circulant graphs either allowing or not allowing perfect state transfer
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DOI：
10.1016/j.aml.2009.04.007
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发表时间：
2009-10
期刊：
影响因子：
--
通讯作者：
Milan B. Tasic;M. Petković
中科院分区：
文献类型：
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作者：
Milan B. Tasic;M. Petković
Saxena、Severini和Shparlinski最近研究了基于积分循环图的量子自旋网络中完美态转移的存在性。在上述工作的激励下，Bašić， petkoviki和stevanovic给出了积分循环图的简单条件，允许其特征值的完美状态转移。他们指出，除了酉Cayley图外，允许完美状态转移的最小顶点的积分循环图是ICG8（{1,2}）和ICG8（{1,4}）。此外，还推测了两类积分循环图ICGn（{1,n/4}）和ICGn（{1,n/2}）在n∈8N时允许PST。这些猜想在这项工作中得到了证实。此外，还证明了在顶点数为无平方整数的图类中不存在允许完全状态转移的积分循环图。
The existence of perfect state transfer in quantum spin networks based on integral circulant graphs has been considered recently by Saxena, Severini and Shparlinski. Motivated by the aforementioned work, Bašić, Petković and Stevanović give the simple condition for the characterization of integral circulant graphs allowing the perfect state transfer in terms of its eigenvalues. They stated that the integral circulant graphs with minimal vertices allowing perfect state transfer, other than unitary Cayley graphs, are ICG8({1,2}) and ICG8({1,4}). Moreover, it is also conjectured that two classes of integral circulant graphs ICGn({1,n/4}) and ICGn({1,n/2}) allow PST where n∈8N. These conjectures are confirmed in this work. Moreover, it is shown that there are no integral circulant graphs allowing perfect state transfer in the class of graphs where the number of vertices is a square-free integer.