Geodesic
Some results for the periodicity and perfect state transfer
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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Let $G$ be a graph with adjacency matrix $A$, let $H(t)=\exp(itA)$. $G$ is called a 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 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.
DOI : 10.37236/671
Classification : 05C50, 81P68
Mots-clés : periodic graph 
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     author = {Jiang Zhou and Changjiang Bu and Jihong Shen},
     title = {Some results for the periodicity and perfect state transfer},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/671},
     zbl = {1229.05205},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/671/}
}
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Jiang Zhou; Changjiang Bu; Jihong Shen. Some results for the periodicity and perfect state transfer. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/671

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