扭曲类超立方体网络THLN的容错路径嵌入
Fault-Tolerant Path-Embedding of Twisted Hypercube-Like Networks THLNs
摘要：
扭曲超立方体网络（$THLNs$）包含几个重要的超立方体变体。本文研究$n$维（$n$ - $D$）$THLNs$的容错路径嵌入问题。令$G_n$是$n$ - $D$ $THLN$，$F$是具有$|F|\leq n-2$的$V(G_n)\cup E(G_n)$的子集.本文证明了对于任意两个不同的正确顶点$u$和$v$，存在一条无故障路径$P_{uv}$，其长度为$l$，且具有$2^{n-1}-1\leq l\leq 2^n-f_v-1-α$，其中$α=0$是指$u$和$v$在$G_n-F$（$n\geq5$）中形成一个正常顶点对，$α=1$是指$u$和$v$在$G_n-F$（）中形成一个弱顶点对.
英文摘要：
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 $V(G_n)\cup E(G_n)$ with $|F|\leq n-2$. We show that for arbitrary two different correct vertices $u$ and $v$, there is a faultless path $P_{uv}$ of every length $l$ with $2^{n-1}-1\leq l\leq 2^n-f_v-1-α$, 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 $G_n-F$($n\geq5$).
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