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Let n be a positive integer, and let Hn denote the graph whose vertex set is...

Let n be a positive integer, and let Hn denote the graph whose vertex set is the set of all n-tuples with coordinates in {0, 1}, such that vertices u and v are adjacent if and only if they differ in one position. For example, if n = 3, then (0, 0, 1) and (0, 1, 1) are adjacent, but (0, 0, 0) and (0, 1, 1) are not. Answer the following with brief justification (formal proofs not necessary):

a. How many vertices does Hn have? (As a function of n.)

b. How many edges does Hn have? (As a function of n.)

c. Is Hn bipartite? (Why or why not?)

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