Perfect State Transfer on NEPS of the path P3

Abstract: Perfect state transfer is significant in quantum communication networks. There are very few graphs having this property. So, it is useful to find some new graphs having perfect state transfer. A good way to construct new graphs is by forming NEPS. It is known that the graph $P_{3}$ exhibits perfect state transfer and so we investigate some NEPS of the path $P_{3}$. A sufficient condition is found for a NEPS of $P_{3}$ to have perfect state transfer. Using these NEPS, some other graphs are constructed having perfect state transfer. We also prove that for every $n\in \Nl\setminus \left\lbrace 1\right\rbrace$ and any odd positive integer $k< n$, there is a basis $\Omega$ such that $NEPS(P_{3},\ldots, P_{3};\Omega)$ is connected and exhibits perfect state transfer.