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Let $G$ be a graph with adjacency matrix $A$. The transition matrix of $G$relative to $A$ is defined by $H_{A}(t):=\exp{(-itA)},\;t\in\Rl$. We say thatthe graph $G$ admits perfect state transfer between the verteices $u$ and $v$at $\tau\in\Rl$ if the $uv$-th entry of $H_{A}(\tau)$ has unit modulus. Perfectstate transfer is a rare phenomena so we consider an approximation calledpretty good state transfer. We find that NEPS (Non-complete Extended P-Sum) ofthe path on three vertices with basis containing tuples with hamming weights ofboth parities do not exhibit perfect state transfer. But these NEPS admitpretty good state transfer with an additional condition. Further we investigatepretty good state transfer on Cartesian product of graphs and we find that agraph can have PGST from a vertex $u$ to two different vertices $v$ and $w$.

Pretty Good State Transfer on Some NEPS