Fault-Tolerant Path-Embedding of Twisted Hypercube-Like Networks THLNs

06/12/2019

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by   Huifeng Zhang, et al.

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The twisted hypercube-like networks(THLNs) contain several important hypercube variants. This paper is concerned with the fault-tolerant path-embedding of n-dimensional(n-D) THLNs. Let G_n be an n-D THLN and F be a subset of V(G_n)∪ E(G_n) with |F|≤ n-2. We show that for arbitrary two different correct vertices u and v, there is a faultless path P_uv of every length l with 2^n-1-1≤ l≤ 2^n-f_v-1-α, where α=0 if vertices u and v form a normal vertex-pair and α=1 if vertices u and v form a weak vertex-pair in G_n-F(n≥5).