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

Authors:
Lun-Min Shih;Chieh-Feng Chiang;Lih-Hsing Hsu;Jimmy J. M. Tan
Affiliations:
Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan 30050, ROC;Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan 30050, ROC;Department of Computer Science and Information Engineering, Providence University, Taichung, Taiwan 43301, ROC;Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan 30050, ROC
Venue:
Information Processing Letters
Year:
2008

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Abstract

In this paper, we study the Menger property on a class of hypercube-like networks. We show that in all n-dimensional hypercube-like 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.