Super-Mixed-Connected Line Digraphs

Abstract

A digraph \(D\) is said to be \({super-mixed-connected}\) if every minimum general cut of \(D\) is a local cut. In this paper, we characterize non-super-mixed-connected line digraphs. As a consequence, if \(D\) is a super-arc-connected digraph with \(\delta(D) \geq 3\), then the \(n\)-th iterated line digraph of \(D\) is super-mixed-connected for any positive integer \(n\). In particular, the Kautz network \(K(d,n)\) is super-mixed-connected for \(d \neq 2\), and the de Bruijn network \(B(d,n)\) is always super-mixed-connected.