Strongly regular graphs with no triangles: challenges and computer algebra results Matan Ziv-Av A strongly regular graph (briefly SRG) with parameters (v,k,\lambda,\mu) is a regular graph of valency k such that every two neighours have exactly \lambda common neighbours, and every two non-neighbours have exactly \mu common neighbours. An SRG is called primitive if both the graph and its complement are connected. We consider primitive SRGs with no triangles (that is \lambda=0, briefly called tfSRGs). The most famous SRG with no triangles, denoted by NL_2(10), has parameters (100, 22, 0, 6), it was described in the paper by Higman and Sims in 1968 in the course of the discovery of a new sporadic simple group HS. Twelve years earlier, Dale Mesner Constructed this graph, Denoting it by NL_2(10). Mesner constructed NL_2(10) by way of an equitable partition of this graph. This construction raises two enumeration problems relating to tfSRGs. One is embedding smaller tfSRGs in larger ones, and the other is equitable paritions of tfSRGS. We present complete computer aided enumeration of embeddings of tfSRGs inside known tfSRGs, and computer aided emumeration of equitable partitions of tfSRG of size up to 50.