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 $\delta (D)\ge 3$, 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 $d\ne 2$, and the de Bruijn network $B(d,n)$ is always super-mixed-connected.