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{\bf Jiang Zhou, Changjiang Bu and Jihong Shen}
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{\bf Some Results for the Periodicity and Perfect State Transfer}
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Let $G$ be a graph with adjacency matrix $A$, let $H(t)=\exp(itA)$. $G$ is called a \textit{periodic graph} if there exists a time $\tau$ such that $H(\tau)$ is diagonal. If $u$ and $v$ are distinct vertices in $G$, we say that \textit{perfect state transfer} occurs from $u$ to $v$ if there exists a time $\tau$ such that $|H(\tau)_{u,v}|=1$. A necessary and sufficient condition for $G$ is periodic is given. We give the existence for the perfect state transfer between antipodal vertices in graphs with extreme diameter.

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