AMS classifications: 05C50, 05E99;

2000 Mathematics Subject Classification: 05C50, 05E99;

AMS classification: 05C50;

AMS classifications; 05C50; 05E30;

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; 51E12

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;

In this paper, we begin the determination of all primitive strongly regular graphs with chromatic number equal to 5.Using eigenvalue techniques, we show that there are at most 43 possible parameter sets for such a graph.For each parameter set, we must decide which strongly regular graphs, if...