Answer the following questions: a.Suppose that a connected bipartite planar simple graph has e edges and v vertices. Show that e ≤ 2v − 4 if v ≥ 3. b. Let G be a graph with n − 1 edges. Show that the...

Answer the following questions:

a.Suppose that a connected bipartite planar simple graph has e edges and v vertices. Show that e ≤ 2v − 4
if v ≥ 3.

b. Let G be a graph with n − 1 edges. Show that the following three statements are equivalent:
(i) G is connected
(ii) G is acyclic;
(iii) G is a tree.