When can one see from the spectrum of a graph whether it is distance-regular or not?We give some new results for when this is the case.As a consequence we find (among others) that the following distance-regular graphs are uniquely determined by their spectrum: The collinearity graphs of the...

AMS classifications: 05E30; 05B20; 94B05

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; 05C50; 05E30;

AMS classifications: 05C50, 05E99;

2000 Mathematics Subject Classification: 05C50, 05E99;

AMS classsifications: 05C50; 05E99; 94C15;

We determine the graphs with maximal spectral radius among the ones on n nodes with diameter D.

AMS classifications: 05E30; 05B20;