A family of resolvable regular graph designs

A regular graph design RGD(v,k;r) is a design on v points with blocks of size k and constant replication number r, such that any two points belong to either λ1 or λ1 + 1 common blocks, for some constant λ1. We investigate resolvable regular graph designs with block size 4. In particular we determine the parameters for which such designs exist, for v⩽ 16.