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Question: recall that a graph is called regular if every vertex...

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Recall that a graph is called regular if every vertex has the same degree.

(a) Let G be an unknown simple regular graph with at least 3 vertices. Suppose you are 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?

(b) Let G be a simple graph with at least 3 vertices. Given the n vertex-deleted subgraphs of G (but not G itself), how can you determine whether or not G is a regular graph?

(c) How can you use (a) and (b) to show that regular graphs are reconstructible.

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