Assume the result is true for all connected plane graphs with fewer than e edges, e21, and suppose g has e edges. If g is a tree. then n=e+l and f=1. so the result holds If g is not a tree. let e be an edge of a cycle of g and consider g-e Clearly, G-e is a connected plane graph with n vertices, e-l edges and f-1 regions, so by the induction hypothesis, n- (e-1)+(f-1)=2, from which it follows that n -e +f=2▪ Assume the result is true for all connected plane graphs with fewer than e edges, ▪ e ≥ 1, and suppose G has e edges. ▪ If G is a tree, then n =e+1 and f= 1, so the result holds. If G is not a tree, let e be an edge of a cycle of G and consider G-e. Clearly, G-e is a connected plane graph with n vertices, e-1 edges and f-1 regions, so by the induction hypothesis, n- (e-1) + (f- 1) = 2, from which it follows that n -e +f = 2