# Turán graph

In mathematical graph theory, the**Turán graph**for given natural numbers

*n*and

*k*, denoted

*T*(

*n*,

*k*), is defined as the extremal graph with

*n*vertices which does not contain the complete graph

*K*

_{k}as a subgraph. An upper bound for the number of edges of

*T*(

*n*,

*k*), typically written as

*t*(

*n*,

*k*), is given by Turán's theorem; as a special case, for

*k*= 3, one obtains