# Graph Theory: Complement of a Graph

1. Nov 17, 2009

### jack_bauer

I'm wondering, is it possible a graph G and its complement G' to be complete?

2. Nov 17, 2009

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.

3. Nov 17, 2009

### letmeknow

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?

4. Nov 17, 2009

### CRGreathouse

Sure, for K_0 and K_1.

5. Oct 13, 2010