Integral graph

In the mathematical field of graph theory, an integral graph is a graph whose spectrum consists entirely of integers. In other words, a graphs is an integral graph if all the eigenvalues of its characteristic polynomial are integers.[1]

The notion was introduced in 1974 by Harary and Schwenk.[2]



  1. Weisstein, Eric W. "Integral Graph". MathWorld.
  2. Harary, F. and Schwenk, A. J. "Which Graphs have Integral Spectra?" In Graphs and Combinatorics (Ed. R. Bari and F. Harary). Berlin: Springer-Verlag, pp. 4551, 1974.
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