The ratio of graduating seniors that go on to college to those who do not is 7:4. This can be written as:
C/N = 7/4
Last year, 28 students went to college, so C = 28. We can substitute this into the ratio:
28/N = 7/4
To solve for N, we can cross-multiply:
28 * 4 = 7 * N
112 = 7N
N = 112 / 7
N = 16
So, 16 students did not go to college.
The total number of graduating seniors is the sum of those who went to college and those who did not:
Total = C + N = 28 + 16 = 44
Therefore, the graduating class size was $\boxed{44}$.