Pretty good state transfer on some NEPS
Pretty good state transfer on some NEPS
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DOI：
10.1016/j.disc.2016.11.026
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发表时间：
2016-04
期刊：
影响因子：
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通讯作者：
Hiranmoy Pal;B. Bhattacharjya
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文献类型：
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作者：
Hiranmoy Pal;B. Bhattacharjya
设 G 是一个具有邻接矩阵 A 的图。G 相对于 A 的转移矩阵由 H A (t)≔ exp (− i t A), t∈ R 定义。如果 H A (τ) 的第 u v 项具有单位模数，则图 G 允许在 τε R 处的顶点 u 和 v 之间进行完美状态转移。完美的状态转移是一种罕见的现象，因此我们考虑一种称为相当好的状态转移的近似值。我们发现三个顶点上的路径的 NEPS（非完全扩展 P-Sum），其基础包含具有两个奇偶校验的汉明权重的元组，并没有表现出完美的状态转移。但这些 NEPS 承认相当好的状态转移，但有一个附加条件。进一步，我们研究了图的笛卡尔积上相当好的状态转移，我们发现图可以具有从顶点 u 到两个不同顶点 v 和 w 的 PGST。
Let G be a graph with adjacency matrix A. The transition matrix of G relative to A is defined by H A (t)≔ exp (− i t A), t∈ R. We say that the graph G admits perfect state transfer between the vertices u and v at τ∈ R if the u v th entry of H A (τ) has unit modulus. Perfect state transfer is a rare phenomenon so we consider an approximation called pretty good state transfer. We find that NEPS (Non-complete Extended P-Sum) of the path on three vertices with basis containing tuples with hamming weights of both parities does not exhibit perfect state transfer. But these NEPS admit pretty good state transfer with an additional condition. Further we investigate pretty good state transfer on Cartesian product of graphs and we find that a graph can have PGST from a vertex u to two different vertices v and w.