Let V = {a,b,c,d} and E = {(a,b),(a,c),(a,d),(d,c)}. Count the number of subgraphs of the graph G = (V,E). (6 Points) (b) Draw a simple, connected, undirected graph consisting of 1 vertex of degree 1, 2 vertices of degree 2, 3 vertices of degree 3, and 4 vertices of degree 4. Is the graph you draw planar or not? Justify your answer. (4 Points) (c) How many simple, undirected graphs that do not contain any cycle can you construct with a fixed vertex set {A,B,C,D,E}? Explain your answer. (6 Points) (d) The diameter of a graph is defined to be the length of the shortest path between the most distanced vertices. What is the diameter of the graph you drew in Question (b)