Lecture 5, slide 16

In order to prove an approximability result for this problem, we have to define the square graph of graph G.
Given a graph G, we define this square graph G as the following graph. We have one copy of the graph for each node of the original graph and then we have an edge between a node in a copy and another node in another copy, if there was an edge between the two nodes corresponding to the two copies.
So this is the formal definition. And it is easy to prove that the original graph has a clique of size k if and not if the square graph has a clique of size k².