AMS classifications: 05E30; 51E12

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.

AMS classification: 05C50;

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.