What is the Complement of a Graph? | Graph Theory, Graph Complements, Self Complementary Graphs

What is the complement of a graph? What are self complementary graphs? We'll be answering these questions in today's video graph theory lesson!

If G is a graph, the complement of G has the same vertex set but the "opposite" edge set. That means two vertices are adjacent in G Complement if and only if they are not adjacent in G. So where there is an edge in G, there is not an edge in G complement. Where there is not an edge in G, there is an edge in G complement.

If a graph is isomorphic to its complement, we say that graph is self complementary. Pretty cool!

In the lesson we go over the fact that if a graph is disconnected then its complement is connected. The converse of this statement is not true. If a graph is connected, its complement is not necessarily disconnected. Consider the path graph on 4 vertices.



I hope you find this video helpful, and be sure to ask any questions down in the comments!

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