A graph \(G\) is \(H\) -free if \(G\) contains no copy of \(H\) as a subgraph. The Turán number of \(H\) , \(\textrm{ex}(n, H)\) , is the maximum number of edges over all \(H\) -free graphs on \(n\) vertices. Let \(\textrm{EX}(n, H)\) be the collection of all \(H\) -free graphs on \(n\) vertices with \(\textrm{ex}(n, H)\) edges. Recently, Chen et al. determined the value of \(\textrm{ex}(n, 2K_{p+ 1})\) . Zhang and also Zhang and Yin determined the value of \(\textrm{ex}(n, 3K_{p+ 1})\) . Hu determined the value of \(\textrm{ex}(n, K_{p+ 1}\cup K_{q})\) for all \(p\ge q\) . In this paper, we characterize \(\textrm{EX}(n, K_{p+ 1}\cup K_{q})\) for all \(p\ge q\) .
