The $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity of hypercubes
At present, the reliability of interconnection networks of multiprocessing systems has become a hot topic of research concern for parallel computer systems. Conditional connectivity is an important parameter to measure the reliability of an interconnected network. In reality, the failure of one node...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-08-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231267?viewType=HTML |
| _version_ | 1797687840195215360 |
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| author | Bo Zhu Shumin Zhang Huifen Ge Chengfu Ye |
| author_facet | Bo Zhu Shumin Zhang Huifen Ge Chengfu Ye |
| author_sort | Bo Zhu |
| collection | DOAJ |
| description | At present, the reliability of interconnection networks of multiprocessing systems has become a hot topic of research concern for parallel computer systems. Conditional connectivity is an important parameter to measure the reliability of an interconnected network. In reality, the failure of one node will inevitably have a negative impact on the surrounding nodes. Often it is the specific structures that fail in an interconnected network. Therefore, we propose two novel kinds of connectivity, called $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity, to go for a more accurate measure of the reliability of the network. Hypercube network is the most dominant interconnection network topology used by computer systems today, for example, the famous parallel computing systems Cray $ T3D $, Cray $ T3E $, $ IBM $ Blue Gene, etc. are built with it as the interconnection network topology. In this paper, we obtain the results of the $ g $-extra $ H $-structure connectivity and the $ g $-extra $ H $-substructure connectivity of the hypercubes when the specific structure is $ P_k $ and $ g = 1 $. |
| first_indexed | 2024-03-12T01:22:51Z |
| format | Article |
| id | doaj.art-dd126c20e37740eea850023ea489fcc7 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-12T01:22:51Z |
| publishDate | 2023-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-dd126c20e37740eea850023ea489fcc72023-09-13T01:20:14ZengAIMS PressAIMS Mathematics2473-69882023-08-01810248482486110.3934/math.20231267The $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity of hypercubesBo Zhu 0Shumin Zhang1Huifen Ge2Chengfu Ye 31. Department of Computer, Qinghai Normal University, Xining, Qinghai 810008, China2. School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, China 3. Academy of Plateau Science and Sustainability, People's Government of Qinghai Province and Beijing Normal University, China2. School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, China2. School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, China 3. Academy of Plateau Science and Sustainability, People's Government of Qinghai Province and Beijing Normal University, ChinaAt present, the reliability of interconnection networks of multiprocessing systems has become a hot topic of research concern for parallel computer systems. Conditional connectivity is an important parameter to measure the reliability of an interconnected network. In reality, the failure of one node will inevitably have a negative impact on the surrounding nodes. Often it is the specific structures that fail in an interconnected network. Therefore, we propose two novel kinds of connectivity, called $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity, to go for a more accurate measure of the reliability of the network. Hypercube network is the most dominant interconnection network topology used by computer systems today, for example, the famous parallel computing systems Cray $ T3D $, Cray $ T3E $, $ IBM $ Blue Gene, etc. are built with it as the interconnection network topology. In this paper, we obtain the results of the $ g $-extra $ H $-structure connectivity and the $ g $-extra $ H $-substructure connectivity of the hypercubes when the specific structure is $ P_k $ and $ g = 1 $.https://www.aimspress.com/article/doi/10.3934/math.20231267?viewType=HTMLconditional connectivity$ g $-extra $ h $-structure connectivity$ g $-extra $ h $-substructure connectivityhypercube |
| spellingShingle | Bo Zhu Shumin Zhang Huifen Ge Chengfu Ye The $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity of hypercubes AIMS Mathematics conditional connectivity $ g $-extra $ h $-structure connectivity $ g $-extra $ h $-substructure connectivity hypercube |
| title | The $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity of hypercubes |
| title_full | The $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity of hypercubes |
| title_fullStr | The $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity of hypercubes |
| title_full_unstemmed | The $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity of hypercubes |
| title_short | The $ g $-extra $ H $-structure connectivity and $ g $-extra $ H $-substructure connectivity of hypercubes |
| title_sort | g extra h structure connectivity and g extra h substructure connectivity of hypercubes |
| topic | conditional connectivity $ g $-extra $ h $-structure connectivity $ g $-extra $ h $-substructure connectivity hypercube |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231267?viewType=HTML |
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