Summary: The connectivity and diagnosability of a multiprocessor system and an interconnection network are two important research topics. The system and the network have an underlying topology, which is usually presented by a graph. As a topology structure of interconnection networks, the \(n\)-dimensional leaf-sort graph \(C F_n\) has many good properties. In this paper, we prove that (a) \(C F_n\) is tightly \(\frac{ 3 n - 3}{ 2}\) super connected for odd \(n\) and \(n\geq4\), and tightly \(\frac{ 3 n - 4}{ 2}\) super connected for even \(n\) and \(n\geq4\); (b) under the PMC model and MM\(^\ast\) model, the diagnosability \(t(C F_n)=\frac{ 3 n - 3}{ 2}\) for odd \(n\) and \(n\geq4\), and \(t(C F_n)=\frac{ 3 n - 4}{ 2}\) for even \(n\) and \(n\geq4\).