The construction of a dual D(G) can be applied in any planegraph G: draw a vertex of D(G) in the middle of each region of Gand draw an edge e* of D(G) perpendicular to each edge e of G; e*connects the vertices of D(G) representing the regions on eitherside of e.
a) A dual need not be a graph. It might have two edges betweenthe same pair of vertices or a self-loop edge (from a vertex toitself). find two planar graphs with duals that are not graphsbecause they contain these two forbidden situations.
C) Show that the degree of a vertex in dual graph D(G) equalsthe number of boundary edges of the corresponding region in theplanar graph G.
E) show for any plane depiction of a graph G that the verticesof G correspond to regions in D(G)
