A vertex listing of a graph G(V, E) is an ordering of the vertices such that consecutive vertices in the ordering are adjacent in the graph. Lets consider a Qn Vertex Listing: this is a vertex listing of the vertices of Qn starting from the vertex labeled with all 0 bits such that no vertex is repeated and all vertices are included in the listing exactly once. For example, the Q1 vertex listing is 0, 1. A Q2 vertex listing is 00, 01, 11, 10. A Q3 vertex listing is 000, 001, 011, 010, 110, 111, 101, 100. (a) (5 points) Provide an iterative algorithm to produce a Qn Vertex Listing. (b) (5 points) Prove the correctness of your iterative Qn Vertex Listing Algorithm. (c) (5 points) Provide a recursive algorithm to produce a Qn Vertex Listing. (It is fine if some iteration is used as well, but there must be at least one recursive call for any case that is not a base case.) (d) (5 points) Prove the correctness of your recursive algorithm Qn Vertex Listing