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The transition matrix of $G$ is denoted by $H(t)$ and it is defined by $H(t):=\\exp{\\left(itA\\right)},\\;t\\in\\mathbb{R}.$ The graph $G$ has perfect state transfer (PST) from a vertex $u$ to another vertex $v$ if there exist $\\tau\\left(\\neq0\\right)\\in\\mathbb{R}$ such that the $uv$-th entry of $H(\\tau)$ has unit modulus. In case when $u=v$, we say that $G$ is periodic at the vertex $u$ at time $\\tau$. The graph $G$ is said to be periodic if it is periodic at all vertices at the same time. 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The transition matrix of $G$ is denoted by $H(t)$ and it is defined by $H(t):=\\exp{\\left(itA\\right)},\\;t\\in\\mathbb{R}.$ The graph $G$ has perfect state transfer (PST) from a vertex $u$ to another vertex $v$ if there exist $\\tau\\left(\\neq0\\right)\\in\\mathbb{R}$ such that the $uv$-th entry of $H(\\tau)$ has unit modulus. In case when $u=v$, we say that $G$ is periodic at the vertex $u$ at time $\\tau$. The graph $G$ is said to be periodic if it is periodic at all vertices at the same time. 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