Edge-bipancyclicity of conditional faulty hypercubes

碩士 === 國立交通大學 === 資訊科學與工程研究所 === 94 === Xu et al. showed that for any set of faulty edges F of an n-dimensional hypercube Qn with |F|≦n-1, each edge of Qn-F lies on a cycle of every even length from 6 to 2n, n≧4, provided not all edges in F are incident with the same vertex. In this paper, we find t...

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Main Authors: Sheng-kai Wang, 王聖凱
Other Authors: Jimmy J.M. Tan
Format: Others
Language:en_US
Published: 2006
Online Access:http://ndltd.ncl.edu.tw/handle/10130205784438624928
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spelling ndltd-TW-094NCTU53940242016-05-27T04:18:34Z http://ndltd.ncl.edu.tw/handle/10130205784438624928 Edge-bipancyclicity of conditional faulty hypercubes 條件式容錯超立方體下的邊泛迴圈之研究 Sheng-kai Wang 王聖凱 碩士 國立交通大學 資訊科學與工程研究所 94 Xu et al. showed that for any set of faulty edges F of an n-dimensional hypercube Qn with |F|≦n-1, each edge of Qn-F lies on a cycle of every even length from 6 to 2n, n≧4, provided not all edges in F are incident with the same vertex. In this paper, we find that under similar condition, the number of faulty edges can be much greater and the same result still holds. More precisely, we show that, for up to |F|=2n-5 faulty edges, each edge of the faulty hypercube Qn-F lies on a cycle of every even length from 6 to 2n with each vertex having at least two healthy edges adjacent to it, for n≧3. Moreover, this result is optimal in the sense that the result can not be guaranteed, if there are 2n-4 faulty edges. Jimmy J.M. Tan 譚建民 2006 學位論文 ; thesis 24 en_US
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language en_US
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description 碩士 === 國立交通大學 === 資訊科學與工程研究所 === 94 === Xu et al. showed that for any set of faulty edges F of an n-dimensional hypercube Qn with |F|≦n-1, each edge of Qn-F lies on a cycle of every even length from 6 to 2n, n≧4, provided not all edges in F are incident with the same vertex. In this paper, we find that under similar condition, the number of faulty edges can be much greater and the same result still holds. More precisely, we show that, for up to |F|=2n-5 faulty edges, each edge of the faulty hypercube Qn-F lies on a cycle of every even length from 6 to 2n with each vertex having at least two healthy edges adjacent to it, for n≧3. Moreover, this result is optimal in the sense that the result can not be guaranteed, if there are 2n-4 faulty edges.
author2 Jimmy J.M. Tan
author_facet Jimmy J.M. Tan
Sheng-kai Wang
王聖凱
author Sheng-kai Wang
王聖凱
spellingShingle Sheng-kai Wang
王聖凱
Edge-bipancyclicity of conditional faulty hypercubes
author_sort Sheng-kai Wang
title Edge-bipancyclicity of conditional faulty hypercubes
title_short Edge-bipancyclicity of conditional faulty hypercubes
title_full Edge-bipancyclicity of conditional faulty hypercubes
title_fullStr Edge-bipancyclicity of conditional faulty hypercubes
title_full_unstemmed Edge-bipancyclicity of conditional faulty hypercubes
title_sort edge-bipancyclicity of conditional faulty hypercubes
publishDate 2006
url http://ndltd.ncl.edu.tw/handle/10130205784438624928
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