Weird: some graphs arc actually isomorphic to their complements! Let\'s explore:

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Weird: some graphs arc actually isomorphic to their complements! Let's explore: Show that P_4 bar P_4. What's another simple example of a graph that is isomorphic to its own complement, which we found in class? You might ask if the graphs from part (a) are the only ones with that peculiar property. The answer is no. To see this, use a proof by induction to build an infinite sequence of graphs where each is isomorphic to its complement! Draw a graph with 13 vertices that is isomorphic to its complement. Without actually drawing the complement, how do you know that this actually works out? Notice that the graphs above are all connected. So now I'm wondering: can a disconnected graph be isomorphic to its complement?

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