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State transfer on graphs. (English) Zbl 1232.05123
Summary: If \(X\) is a graph with adjacency matrix \(A\), then we define \(H(t)\) to be the operator \(\exp(A)\). We say that we have perfect state transfer in \(X\) from the vertex \(u\) to the vertex \(v\) at time \(\tau\) if the \(uv\)-entry of \(|H(\tau )_{u,v}|=1\). State transfer has been applied to key distribution in commercial cryptosystems, and it seems likely that other applications will be found. We offer a survey of some of the work on perfect state transfer and related questions. The emphasis is almost entirely on the mathematics.

MSC:
05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C90 Applications of graph theory
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