Question: Problem 1. The ndimensional hypercube is the graph H with vertex set V = {0, 1} (Le. every nbit string is a vertex of H),

Problem 1. The ndimensional hypercube is the graph H\" with vertex set V = {0, 1}\" (Le. every nbit string is a vertex of H\"), where two vertices are connected by an edge if and only if they differ in exactly one bit. For example, here is a picture of H3: 001 011 111 000 10! 110 a) Prove that any two spanning trees of H3 share at least one edge. b) Show that for any two vertices 15,11 6 H 3, if u 75 12 then there are three paths from u to 12 that have no vertices in common (except for u and v, of course). c) Show that H3 is 3-connected. d) Extend parts (b) and (c) to H4. What do you think happens for H\

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