Computer algebra investigation of known primitive triangle-free strongly regular graphs

With the aid of computer algebra systems COCO and GAP with its packages we are investigating all seven known primitive triangle-free strongly regular graphs on 5, 10, 16, 50, 56, 77 and 100 vertices. These graphs are rank 3 graphs, having a rich automorphism group. The embeddings of each graph from this family to other ones are described, the automorphic equitable partitions are classified, all equitable partitions in the graphs on up to 50 vertices are enumerated. Basing on the reported computer aided results and using techniques of coherent configurations, a few new models of these graphs are suggested, which are relying on knowledge of just a small part of symmetries of a graph in consideration.