Let G be a simple graph with n vertices Show that a G is a t

Let G be a simple graph with n vertices. Show that

a) G is a tree if and only if it is connected and has n 1 edges.

b) G is a tree if and only if G has no simple circuits and has n 1 edges. [Hint: To show that G is connected if it has no simple circuits and n 1 edges, show that G cannot have more than one connected component.]

Solution