Question: Given a simple graph G = (V, E), its complement graph Gc = (V, Ec) is the graph with the same vertex set and edge

Given a simple graph G = (V, E), its complement graph Gc = (V, Ec) is the graph with the same vertex set and edge set Ec = {{u, v} : u, v V, {u, v} / E}. (a) Show that G and Gc cannot both be disconnected. Construct an example for which G and Gc are both connected. (b) Show that if |V | 11, then G and Gc cannot both be planar

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