For maximum marks, you were expected to address both parts of the problem in your report and do something about the first part.
One of the post-conditions of your MST method should have been:
The tree produced is a spanning tree.Adding an additional method SpanningTree( Graph g ) to your graph class and using it as the post-condition for MST is the best approach.
You can then simply run the MST method on a number of carefully chosen graphs and if the post-condition assertion is never raised (except perhaps for deliberate error inputs, such as disjoint graphs which don't have a spanning tree at all!) then you can assert that your function is producing a spanning tree at least!