Restricted Arc Connectivity of Unidirectional Hypercubes and Unidirectional Folded Hypercubes

Abstract

Unidirectional hypercubes and unidirectional folded hypercubes are generalizations of hypercubes and folded hypercubes to digraphs. The super-$\lambda$ property of a digraph is a index for network reliability, which can be measured by the restricted arc-connectivity quantitatively. In this paper, we first show that the restricted arc-connectivity of the $n$-dimensional unidirectional hypercube is $n-1$ when $n$ is even and is $n-2$ when $n$ is odd, and then we show that the restricted arc-connectivity of the $n$-dimensional unidirectional folded hypercube is $n-1$ when $n$ is even and is $n$ when $n$ is odd. As a consequence, we prove that both unidirectional hypercube and unidirectional folded hypercube are super-$\lambda$.