Graphs with integral spectrum

Omran Ahmadi, Noga Alon, Ian F. Blake, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review

66 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)547-552
Number of pages6
JournalLinear Algebra and Its Applications
Issue number1
StatePublished - Jan 1 2009
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


  • Cayley graph
  • Graph spectrum
  • Integral eigenvalue
  • Random matrix


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