Graph Theory question.

4. Recall that a graph is called regular if every vertex has the same degree. st 3 vertices. Suppose you given a graph H and you are told that H was obtained from G by deleting one vertex of G. How can you construct G from H? [Be careful to make sure you consider all possible cases in this problem.] (b) Let G be a simple graph with at least 3 vertices. Given the n vertex-deleted subgraphs of G (but not G itsel), how can you determine whether or not G is a regula graph? (c) How can you use (a) and (b) to show that regular graphs are reconstructible