This project aims to obtain results in the mathematical areas of algebraic combinatorics and spectral graph theory using substructures of projective spaces. In particular, applications in divisible design graphs will be examined. Such graphs were introduced by Haemers, Kharaghani and Meulenberg because they form a bridge between (group) divisible designs and graphs. A divisible design graph has six parameters (v,k,a,b,m,n) and is defined as a graph with v vertices where each vertex is adjacent to exactly k other vertices, and such that the vertex set can be divided into n classes of size m such that two vertices of the same class have exactly a common neighbors and such that two vertices of different classes have exactly b common neighbors. It will be examined, among other things, whether it is possible to construct such graphs using substructures of projective spaces.