Building upon the work of Wei and Ge (Designs, Codes, and Cryptography 74, 2015), we extend the range of positive integer parameters g, u, and m for which group divisible designs with block size 4 and type gum1 are known to exist. In particular, we show that the necessary conditions for the existence of these designs when m>0 and m≠g are sufficient in the following cases: g≡0( mod 6), g=2 with one exception, 2651, g=10, and g=11.

The design spectrum has been determined for two of the 15 graphs with six vertices and ten edges. In this paper we completely solve the design spectrum problem for a further eight of these graphs.