Cycles embedding in folded hypercubes with conditionally faulty vertices

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• 作者：Che-Nan Kuo^a ; ^{cn.kuo@mail.toko.edu.tw} ; Yu-Huei Cheng^b ; ^{yuhuei.cheng@gmail.com}
• 关键词：Interconnection networks ; Folded hypercubes ; Cycles ; Conditionally faulty ; Fault-free
• 刊名：Discrete Applied Mathematics
• 出版年：2017
• 出版时间：31 March 2017
• 年：2017
• 卷：220
• 期：Complete
• 页码：55-59
• 全文大小：473 K
• 卷排序：220

文摘

A network is said to be conditionally faulty if its every vertex is incident to at least gg fault-free vertices, where g≥1g≥1. An nn-dimensional folded hypercube FQnFQn is a well-known variation of an nn-dimensional hypercube QnQn, which can be constructed from QnQn by adding an edge to every pair of vertices with complementary addresses. In this paper, we define that a network is said to be gg-conditionally faulty if its every vertex is incident to at least gg fault-free vertices. Then, let FFvFFv denote the set of faulty vertices in FQnFQn, we consider the cycles embedding properties in 44-conditionally faulty FQn−FFvFQn−FFv, as follows: 1.For n≥3n≥3, FQn−FFvFQn−FFv contains a fault-free cycle of every even length from 44 to 2n−2∣FFv∣2n−2∣FFv∣, where |FFv|≤2n−5|FFv|≤2n−5;2.For even n≥4n≥4, FQn−FFvFQn−FFv contains a fault-free cycle of every odd length from n+1n+1 to 2n−2∣FFv∣−12n−2∣FFv∣−1, where |FFv|≤2n−5|FFv|≤2n−5.