As you already know, a clique graph is a set of vertices such that they all are connected to each other. And the maximal clique is a clique which cannot be extended to a larger clique. Formally, it's a clique which is not contained in any other clique. And a maximum clique is a clique of the largest size. And the last piece of notation is the clique number of a graph G, which we denote by little article of G, is the size of a maximum clique in G. Let us see some examples. In this graph, these three vertices form a clique of size three. We'll also call it a triangle. But this clique is not a maximal clique, because it can be extended to a clique of size four. This clique of size three is a maximal clique because there is no way to extend it to a larger clique. And this clique of size four is a maximum clique, because this graph doesn't contain larger cliques, it doesn't contain cliques of size five. Similarly, we can define independent sets. An independent set in a graph is set of vertices such that there are no edges between them. A maximal independent set is an independent set which cannot be extended to a larger one. And again, a maximum independent set is an independent set of the largest size. And the independence number of a graph G, denoted by alpha of G, is the size of a maximum independent set. Now, let's see some examples. Here is an independent set of size two. And this set is not a maximal independent set, because it can actually be extended to an independent set of size three. Here is an independent set of size three, and it is a maximum independence then, because there is no way to extend it to an independent set of size four. And this is a maximum independent set. This is an independent set of size four, which is the largest one in this specific graph. So the independence number of this graph is four. We already saw a connection between cliques in a graph and independent sets and its complement. Let's just state it one more time formally. If there is a clique in a graph, then there are all edges between those vertices. Then in the complement of this graph, there will be no edges. So, those vertices would form an independent set. Cliques in a graph correspond to independent sets in its complement. And the largest clique, a maximum clique, would correspond to the largest, the maximum independent set in its complement. So the clique number of a graph equals the independence number of its complement. By now a new notation, little omega of G equals alpha of the complement of G.