We study nonregular graphs with three eigenvalues.We determine all the ones with least eigenvalue -2, and give new infinite families of examples.

For most feasible spectra of connected regular graphs with four distinct eigenvalues and at most 30 vertices we find all such graphs, using both theoretic and computer results.

AMS classifications: 05E30; 05B20

2010 Mathematics Subject Classification: 05E30, 05C50;