Classification of divisible design graphs with at most 39 vertices

A $k$-regular graph is called a divisible design (DDG for short) if its vertex set can be partitioned into $m$ classes of size $n$, such that two distinct vertices from the same class have exactly $\lambda_1$ common neighbors, and different $\lambda_2$ neighbors. DDG with $m = 1$, $n or $\lambda_1 \lambda_2$ improper, otherwise it proper. We present new constructions DDGs and, using computer enumeration algorithm, we find all proper connected at most 39 vertices, except three tuples parameters: $(32,15,6,7,4,8)$, $(32,17,8,9,4,8)$, $(36,24,15,16,4,9)$.