Some problems in extremal graph theory and finite geometry

Abstract

This thesis is devoted to the study of several problems in extremal graph theory and finite geometry. We study properties such as girth, spectrum, and automorphism group of various families of algebraically defined graphs. We present a new and shorter proof of the girth of the family of graphs D(n, q). We also determine the asymptotics of the number of cycles of length 2k in the point-line incidence graph of the projective plane.