AMS classification: 05C50, 05C70, 05E30.

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...

AMS classification: 05C50;

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.

The algorithms of inverse iteration and Rayleigh quotient iteration for approximating an eigenpair of a matrix contain a step in which a matrix-vector equation must be solved.The behaviour of these algorithms is analysed if this equation is solved only approximately with a known tolerance.