A plane graph is self-dual if it is isomorphic to its dual graph. Prove that if G is self-dual, then $|E(G)| = 2|V(G)| - 2$. (Hint: use Euler's Formula and the relation between a plane graph and its dual graph.)
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Now, let's consider a self-dual graph G. By definition, G is isomorphic to its dual graph. This means that the number of vertices in G is equal to the number of faces in its dual graph, and vice versa. Let's denote the number of vertices in G as VG and the number Show more…
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