Strong Menger connectivity with conditional faults on the class of hypercube-like networks

Lun-Min Shih; Chieh-Feng Chiang; Lih Hsing Hsu; Jiann-Mean Tan

doi:10.1016/j.ipl.2007.10.009

Strong Menger connectivity with conditional faults on the class of hypercube-like networks

Lun-Min Shih, Chieh-Feng Chiang, Lih Hsing Hsu, Jiann-Mean Tan

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

27 Scopus citations

Abstract

In this paper, we study the Menger property on a class of hypercube-like networks. We show that in all n-dimensional hypercubelike networks with n - 2 vertices removed, every pair of unremoved vertices u and v are connected by min{deg(u), deg(v)} vertex-disjoint paths, where deg(u) and deg(v) are the remaining degree of vertices u and v, respectively. Furthermore, under the restricted condition that each vertex has at least two fault-free adjacent vertices, all hypercube-like networks still have the strong Menger property, even if there are up to 2n - 5 vertex faults. (C) 2007 Elsevier B.V. All rights reserved.

Original language	English
Pages (from-to)	64-69
Number of pages	6
Journal	Information Processing Letters
Volume	106
Issue number	2
DOIs	https://doi.org/10.1016/j.ipl.2007.10.009
State	Published - 15 Apr 2008

Keywords

strong Menger connectivity; conditional faults; hypercube-like network; interconnection networks

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title = "Strong Menger connectivity with conditional faults on the class of hypercube-like networks",

abstract = "In this paper, we study the Menger property on a class of hypercube-like networks. We show that in all n-dimensional hypercubelike networks with n - 2 vertices removed, every pair of unremoved vertices u and v are connected by min{deg(u), deg(v)} vertex-disjoint paths, where deg(u) and deg(v) are the remaining degree of vertices u and v, respectively. Furthermore, under the restricted condition that each vertex has at least two fault-free adjacent vertices, all hypercube-like networks still have the strong Menger property, even if there are up to 2n - 5 vertex faults. (C) 2007 Elsevier B.V. All rights reserved.",

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AU - Chiang, Chieh-Feng

AU - Hsu, Lih Hsing

AU - Tan, Jiann-Mean

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AB - In this paper, we study the Menger property on a class of hypercube-like networks. We show that in all n-dimensional hypercubelike networks with n - 2 vertices removed, every pair of unremoved vertices u and v are connected by min{deg(u), deg(v)} vertex-disjoint paths, where deg(u) and deg(v) are the remaining degree of vertices u and v, respectively. Furthermore, under the restricted condition that each vertex has at least two fault-free adjacent vertices, all hypercube-like networks still have the strong Menger property, even if there are up to 2n - 5 vertex faults. (C) 2007 Elsevier B.V. All rights reserved.

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