Graph Theory: Complement of a Graph

jack_bauer
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I'm wondering, is it possible a graph G and its complement G' to be complete?
 
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Start with the complete graph K_3, and find its complement. What do you notice? Think about the definition of the complement of a graph and think about what would happen in general.
 
A complete graph G on n vertices is a graph that has an edge between any two vertices, no matter which two you pick. The complement of G is a graph of n vertices and is constructed by drawing the n vertices on the paper and then filling in the edges that are not present in G. Which edges are missing in G if G is complete?
 
jack_bauer said:
I'm wondering, is it possible a graph G and its complement G' to be complete?

Sure, for K_0 and K_1.
 
i think you mean G union G' to be complete?
 

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