Pretty good state transfer on some NEPS

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• 作者：Hiranmoy Pal ^{hiranmoy@iitg.ernet.in} ; Bikash Bhattacharjya ; ^{b.bikash@iitg.ernet.in}
• 关键词：Perfect state transfer ; Pretty good state transfer ; NEPS of graphs
• 刊名：Discrete Mathematics
• 出版年：2017
• 出版时间：April 2017
• 年：2017
• 卷：340
• 期：4
• 页码：746-752
• 全文大小：420 K
• 卷排序：340

文摘

Let GG be a graph with adjacency matrix AA. The transition matrix of GG relative to AA is defined by HA(t)≔mo>exp(−itA),t∈R. We say that the graph GG admits perfect state transfer between the vertices uu and vv at τ∈Rτ∈R if the uvuvth entry of HA(τ)HA(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 uu to two different vertices vv and ww.