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June, 2019 Restricted Arc Connectivity of Unidirectional Hypercubes and Unidirectional Folded Hypercubes
Shang-wei Lin, Na-qi Fan
Taiwanese J. Math. 23(3): 529-543 (June, 2019). DOI: 10.11650/tjm/180808

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-$\lambda$.

Citation

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Shang-wei Lin. Na-qi Fan. "Restricted Arc Connectivity of Unidirectional Hypercubes and Unidirectional Folded Hypercubes." Taiwanese J. Math. 23 (3) 529 - 543, June, 2019. https://doi.org/10.11650/tjm/180808

Information

Received: 17 December 2017; Revised: 25 May 2018; Accepted: 23 August 2018; Published: June, 2019
First available in Project Euclid: 31 August 2018

zbMATH: 07068560
MathSciNet: MR3952237
Digital Object Identifier: 10.11650/tjm/180808

Subjects:
Primary: 05C40

Rights: Copyright © 2019 The Mathematical Society of the Republic of China

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Vol.23 • No. 3 • June, 2019
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