The aim of this work is to present the properties of eigenvalues of real symmetric matrices. We are interested in finding the minimum number of distinct eigenvalues $q(G)$ of all matrices whose zero-nonzero pattern belongs to a given graph $G$. For some families of graphs $G$ we calculate $q(G)$. We mention the properties of the join of two graphs and also Cartesian, tensor and strong products of graphs. In particular, we are interested in graphs $G$ on $n$ points, for which $q(G)=1,2, n-1$ or $n$.
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