Is "DG" (Brand) Connected to Dolce& Gabbana?

I have researched both websites, and I cannot tell if they have any relationship-the names are so close I would expect to see some legal issues (if they were separate firms).
Are they?

Are you talking about DG Eyewear? It’s not part of Dolce and Gabbana.

Dollar General?

No, I think he means Data General.