Unfortunately, I haven't seen it in map form yet, but here is the biggest employer for each state:
http://247wallst.com/special-report/2015/03/19/the-largest-employer-in-each-state-2/
A bunch of states had hospital/health systems or university systems where state schools have multiple campuses. And a few states had a unique employer, like Boeing in WA, a food retailer in NJ and MGM in NV. But for the entire Southern block from VA to FL over to TX plus IL & OH, it's Walmart. In VA, it was the ship yards in Tidewater 30 years ago, then Food Lion like 15-20 years ago, now Walmart. Growing up in Balmur, the docks and Beth Steel used to be huge employers, and now it's the U of Md system. It's not like I didn't realize it before, but this state by state list shows quite starkly that we've become a service economy.