A connected graph is called a tree if it has no circuits.
(a) Find the incidence matrix for each of the following directed trees:
(i)

(ii)

(iii)

(iv)

(b) Draw all distinct trees with 4 vertices. Assign a direction to the edges, and write down the corresponding incidence matrices.
(c) Prove that a connected graph on n vertices is a tree if and only if it has precisely n - 1 edges.