An integral graph, not to be confused with an integral embedding of a graph, is defined as a graph whose graph spectrum consists entirely of integers. The
notion was first introduced by Harary and Schwenk (1974). The numbers of simple integral
graphs on ,
2, ... nodes are 0, 2, 3, 6, 10, 20, 33, 71, ... (OEIS A077027),
illustrated above for small .

The numbers of connected simple integral graphs on , 2, ... nodes are 1, 1, 1, 2, 3, 6, 7, 22, 24, 83, ... (OEIS
A064731), illustrated above for small .

The following table lists common graph classes and the their members which are integral.

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. 45-51, 1974.Sloane, N. J. A.
Sequences 064731 A and A077027
in "The On-Line Encyclopedia of Integer Sequences."