Abstract of the master thesis: In this thesis distance-regular graphs and their classical families are introduced. We develop theory, needed for an understanding and research of distance-regular graphs, with an emphasis on the antipodal distance-regular graphs. The main result is a theorem, which gives an upper bound on the valency of an antipodal distance-regular graph with diameter 4 in terms of number of vertices. Also Pyber and Hiraki-Koolen upper bounds for diameter of distance-regular graphs are proved.
Keywords: distance-regular graphs, strongly regular graphs, antipodal distance-regular graphs, quotient graphs, association schemes, Toeplitz matrices.
Math. subj. class (2000): primary 05C12, 05C25, 05C35, 05C50, 05E30