That's a really low budget. Anyway. This is what I could find. You'll have to go through it and see if you find what you're looking for. Most laptops in your price range don't have a dedicated graphics card, they have an integrated one, which means its not separate from the motherboard, it's part of it, therefore the graphics memory will depend on the RAM.
Here are 5 decent laptops in your price range. The first one, the Acer seems like a decent deal.