1-vertex-fault-tolerant cycles embedding on folded hypercubes

Authors:
Sun-Yuan Hsieh;Che-Nan Kuo;Hui-Ling Huang
Affiliations:
Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan 701, Taiwan;Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan 701, Taiwan;Department of Information Management, Southern Taiwan University, No. 1, Nantai Street, Yung-Kang City, Tainan 71005, Taiwan
Venue:
Discrete Applied Mathematics
Year:
2009

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Abstract

In this paper, we focus on a hypercube-like structure, the folded hypercube, which is basically a standard hypercube with some extra links between its nodes. Let f be a faulty vertex in an n-dimensional folded hypercube FQ"n. We show that FQ"n-{f} contains a fault-free cycle of every even length from 4 to 2^n-2 if n=3 and, furthermore, every odd length from n+1 to 2^n-1 if n=2 and n is even.