Classification of divisible design graphs with at most 39 vertices.

A k‐regular graph is called a divisible design graph (DDG) if its vertex set can be partitioned into m classes of size n, such that two distinct vertices from the same class have exactly λ1 common neighbours, and two vertices from different classes have exactly λ2 common neighbours. A DDG with m=1, n=1, or λ1=λ2 is called improper, otherwise it is called proper. We present new constructions of DDGs and, using a computer enumeration algorithm, we find all proper connected DDGs with at most 39 vertices, except for three tuples of parameters: (32,15,6,7,4,8), (32,17,8,9,4,8), and (36,24,15,16,4,9). [ABSTRACT FROM AUTHOR]