Graphs with integral spectrum (Q958042)
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scientific article; zbMATH DE number 5376922
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Graphs with integral spectrum |
scientific article; zbMATH DE number 5376922 |
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Graphs with integral spectrum (English)
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2 December 2008
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It is shown that only a fraction of \(2^{-\Omega(n)}\) of the graphs on \(n\) vertices have an integral spectrum. Although there are several explicit constructions of such graphs, no upper bound for their number has been known. Graphs of this type play an important role in quantum networks supporting the so-called perfect state transfer.
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graph spectrum
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integral eigenvalue
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random matrix
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Cayley graph
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0.90454423
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