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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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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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.
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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 |
work_keys_str_mv |
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