Problem 2. (20 points) Consider G = (V, E) for figure 1 where V is the vertex/nodes and E is the edges.
(Hint: for example, for V = {a,b} and the edge would be E = {ab}.)
(1) Write down set of V and E.
(2) Is G a tree? Explain your reason by checking with the definition of tree.
(3) Write down the adjacent nodes for a and c.
(4) If i is j's adjacent nodes or j is i's adjacent nodes, write the entry of A(i, j) = 1 otherwise A(i, j) = 0.
Write down adjacency matrix A in the order of a, e, h, f, g.