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The graph $G$ is said to have perfect state transfer (PST) from a vertex $u$ to another vertex $v$, if there exist $\\tau\\in\\Rl$ such that the $uv$-th entry of $H(\\tau)$ has unit modulus. The graph $G$ is said to be periodic at $\\tau\\in\\Rl$ if there exist $\\gamma\\in\\Cl$ with $|\\gamma|=1$ such that $H(\\tau)=\\gamma I$, where $I$ is the identity matrix. 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