Taiwanese Journal of Mathematics

Restricted Arc Connectivity of Unidirectional Hypercubes and Unidirectional Folded Hypercubes

Shang-wei Lin and Na-qi Fan

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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-$\lambda$.

Article information

Taiwanese J. Math., Volume 23, Number 3 (2019), 529-543.

Received: 17 December 2017
Revised: 25 May 2018
Accepted: 23 August 2018
First available in Project Euclid: 31 August 2018

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 05C40: Connectivity

network directed graph unidirectional hypercube unidirectional folded hypercube restricted arc-connectivity


Lin, Shang-wei; Fan, Na-qi. Restricted Arc Connectivity of Unidirectional Hypercubes and Unidirectional Folded Hypercubes. Taiwanese J. Math. 23 (2019), no. 3, 529--543. doi:10.11650/tjm/180808. https://projecteuclid.org/euclid.twjm/1535680829

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