Focusing solely on the question of focal length: a football field is about 160 feet wide.
Simply assuming you're on the edge of the field and the graduate is straight across on the other side, assuming you're using a full frame camera you should be able to get a fairly tight shot of the individual with a 2700 mm lens (on a 1.5x crop camera you would only need about an 1800 mm lens).
Unfortunately, you'll likely be in the stands and likely not able to get that close, so lets say you're another 50 feet away for a total of 210 feet from the subject, if the graduate is directly in front of you. You'll need a lens of roughly 3500mm on a full frame camera to get the same fairly tight shot. On a 1.5x crop camera you'll only need about 2400 mm.
Both of those are likely ideal scenarios: with many graduates and families around you likely will be farther away and see many spots you wish you could get to for a photo. Let's round that distance up to 300 ft -- full frame: 5100 mm; crop sensor: 3400 mm.
Canon did make a 5200 mm lens, but it's minimum focus distance is about 400 feet, so that won't work for you. More readily available is Canon's 1200mm. Nikon made a 1200-1700mm zoom lens if you prefer zooms, and also made a 2000mm lens. You may be able to carry some of these by yourself, but probably not when you include the required support equipment. And I'm ignoring costs completely!
Thinking more practically, a nice 300 or 400mm lens will let you get some nice group shots of the many graduates in the field from those distances. Focus on getting a shot of the graduate with diploma after the ceremony where you can pick a location, control the lighting, and prod them for a happy smile.