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Graphs with integral spectrum |
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| Authors: | Omran Ahmadi |
| Affiliation: | a Department of Combinatorics and Optimization, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 b Department of Mathematics, Tel Aviv University, Tel Aviv 69978, Israel c Department of Electrical and Computer Engineering, University of Toronto, Toronto, Ontario, Canada M5S 3G4 d Department of Computing, Macquarie University, Sydney, NSW 2109, Australia |
| Abstract: | It is shown that only a fraction of 2-Ω(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. |
| Keywords: | 05C50 05C80 |
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