I know that the worse case running time of graham scan is O(nlogn) but I am not sure how to generate the worst case data. From what I understood, this occurs at the step where points are being sorted, so does that mean I should generate the worst case data for the sorting algorithm I used?
Any help would be appreciated.
Yes, as Matt notes, you need to generate a worst case for the sorting algorithm, since the rest of the algorithm runs in worst-case linear time. This sorting algorithm should be a comparison sort; otherwise, the lower bound may not be valid.
Unfortunately, without knowing the sorting algorithm, it's difficult to point to specific inputs that trigger the worst case. Some sorts, such as quicksort and mergesort, are best-case Θ(n log n). Others, like Timsort and smoothsort, have linear-time best cases. Unfortunately, given any linear-time procedure that takes a length (in unary) and returns a permutation, there's a sorting algorithm that runs in linear time on those specific permutations by checking whether the input is permuted that way and then falling back to mergesort if necessary.
The best I can do for an unspecified algorithm is to suggest that you choose a uniform random permutation, since every correct comparison sort averages Ω(n log n)-time on this input distribution.
