ON RESTRICTED ARC-CONNECTIVITY OF REGULAR DIGRAPHS

Abstract

The restricted arc-connectivity $\lambda'$ of a strongly connected digraph $G$ is the minimum cardinality of an arc cut $F$ in $G$ such that every strongly connected component of $G-F$ contains at least two vertices. This paper shows that for a $d$-regular strongly connected digraph with order $n$ and diameter $k \geq 4$, if $\lambda'$ exists, then $$ \lambda'(G) \geq \min \left\{ \frac{(n-d^{k-1})(d-1)}{d^{k-1}+d-2},\ 2d-2 \right\}. $$ As consequences, the restricted arc-connectivity of the de Bruijn and Kautz digraph and the generalized de Bruijn and Kautz digraph are determined.