grantor: University of Toronto ; This thesis presents a methodology for the systematic generation of strongly regular graphs by fusing classes in large association schemes; this methodology includes: (1) an algorithm for finding the eigenvalue matrix of an association scheme; (2) an algorithm for determining the lattice of matrices determined by subgroups of the automorphism group of an association scheme; (3) an integer programming formulation that allows us to determine quickly whether a matrix (obtained by fusing the columns of the eigenvalue matrix of an association scheme according to some group) will yield strongly regular graphs with a given parameter set; (4) an exhaustive search algorithm that, given the parameters of a graph and a matrix, will find all the combinations of columns of the matrix that correspond to strongly regular graphs with the given parameters. Using the methodology presented here, we have settled the existence problem for strongly regular graphs with the following parameters: 'srg'(625, 156, 29, 42); 'srg'(1024, 330, 98, 110); 'srg'(729, 308, 127, 132); 'srg'(1024, 363, 122, 132); 'srg'(729, 336, 153, 156); 'srg'(1024, 396, 148, 156); 'srg'(1024, 231, 38, 56); 'srg'(1024, 429, 176, 182); 'srg'(1024, 297, 76, 90); 'srg'(1024, 462, 206, 210). We have also found new graphs for many parameter sets for which some graphs were already known, as well as graphs which were themselves known. Many of the graphs found are pseudo-geometric, i.e., their parameters correspond to those of ...