Let be a graph with graph vertices and graph edges on graph vertices without a -clique. Then
where is the edge count. (Note that the convention of Aigner (1995) of considering -cliques has been replaced with the apparently slightly more standard indexing by considering -cliques, providing consistency with the usual definition of Turán graphs.)
The Turán graph is defined as the unique graph without a -clique having the maximum possible number of graph edges, namely
where denotes the floor function.