Hi,
As other posters have suggested, it very much depends on what you mean by 'graphic design' - it's a broad term. Will you designing books? web sites? business cards? posters? tweaking photos?
If you're serious, and have plenty of cash (and time to learn) then Adobe's Creative Suite (Illustrator, Photoshop, InDesign) is what 99% of all professionals use. Or there are plenty of free - or at least cheaper - apps out there that may do a good enough job for your needs.
Also, remember that having a good computer and software doesn't necessarily make you a good graphic designer! ;-)
Good luck!