Classification of divisible design graphs with at most 39 vertices

Abstract

AbstractA ‐regular graph is called a divisible design graph (DDG) if its vertex set can be partitioned into classes of size , such that two distinct vertices from the same class have exactly common neighbours, and two vertices from different classes have exactly common neighbours. A DDG with , , or 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: , , and .