a Give a planar drawing of the graph with degree sequence (1,1,1,2,3,3,3,3,3,3,3,3,4,4,7). c Disprove the following statement by giving a counter-example. Claim: For every tree T1 = (V, E1) and tree T2 = (V, E2) where | V| > 3 and Ein E2 = ), the graph G= (V, EU E2) is 2-connected. Clearly indicate what T1 and T2 are and motivate why the resulting graph is not 2-connected. = d Let T = (V, E) be a tree with |VI > 3 and k > 2 leaves. Prove that we can add k 1 edges to T to obtain a graph G that is 2-connected