Let G = (V, E) be an undirected graph and let A ? V and B ? V. Show that a N(A ? B) = N(A) ? N(B). b N(A ? B) ? N(A) ? N(B), and give an example where N(A ? B) ? N(A) ? N(B).
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This implies that y is adjacent to a vertex in A and/or a vertex in B. Therefore, y belongs to N(A) and/or N(B), which means y belongs to N(A) ∩ N(B). This shows that N(A ∪ B) is a subset of N(A) ∩ N(B). Conversely, if a vertex y belongs to N(A) ∩ N(B), then y is Show more…
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