In this note, motivated by the non-existence of a vertex-transitive strongly regular graph with parameters , we obtain a feasibility condition concerning strongly regular graphs admitting an automorphism group with exactly two orbits on vertices. We also establish a result on the possible orbit sizes of a potential strongly regular graph with parameters . We use our results to obtain a list of only 11 possible orbit size combinations for a potential strongly regular graph with parameters admitting an automorphism group with exactly two orbits.
