In this BSc thesis we deal with matrix graph theory. We are interested primarily in the eigenvalues of the so-called adjacency matrix of a given graph. Because of that, we present the basic concepts and some basic results from linear algebra and a short introduction to a graph theory. We introduce the concepts of adjacency matrices, eigenvalues and the spectrum of a given graph. We investigate how the properties of a given graph reflect on its spectrum. For the well-known families of graphs we calculated their spectra.
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