Extra Connectivity and Extra Diagnosability of Enhanced Folded Hypercube-like Networks
In the design of multiprocessor systems, evaluating the reliability of interconnection networks is a critical aspect that significantly impacts system performance and functionality. When quantifying the reliability of these networks, extra connectivity and extra diagnosability serve as fundamental m...
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MDPI AG
2025-07-01
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| author | Yihong Wang Cheng-Kuan Lin |
| author_facet | Yihong Wang Cheng-Kuan Lin |
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| description | In the design of multiprocessor systems, evaluating the reliability of interconnection networks is a critical aspect that significantly impacts system performance and functionality. When quantifying the reliability of these networks, extra connectivity and extra diagnosability serve as fundamental metric parameters, offering valuable insights into the network’s resilience and fault-handling capabilities. In this paper, we investigate the 1-extra connectivity and 1-extra diagnosability of the <i>n</i>-dimensional enhanced folded hypercube-like network. Through analysis, we show that the 1-extra connectivity of this network is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn></mrow></semantics></math></inline-formula>. Moreover, for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>></mo><mn>5</mn></mrow></semantics></math></inline-formula>, we determine its 1-extra diagnosability under both the PMC model and the MM<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mo></mo><mo>∗</mo></msup></semantics></math></inline-formula> model to be <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn></mrow></semantics></math></inline-formula>. These results show that as the dimension <i>n</i> increases, both the 1-extra connectivity and 1-extra diagnosability of the network approach approximately twice the value of traditional diagnosability metrics. This provides quantitative insights into the reliability properties of the enhanced folded hypercube-like network, contributing to a better understanding of its performance in terms of connectivity and fault diagnosis. |
| format | Article |
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| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-4e29d1de69564923bd4d4fb8813c55fc2025-08-20T04:00:54ZengMDPI AGMathematics2227-73902025-07-011315244110.3390/math13152441Extra Connectivity and Extra Diagnosability of Enhanced Folded Hypercube-like NetworksYihong Wang0Cheng-Kuan Lin1School of Computer Engineering, Jimei University, Xiamen 361021, ChinaDepartment of Computer Science, National Yang Ming Chiao Tung University, Hsinchu 30010, TaiwanIn the design of multiprocessor systems, evaluating the reliability of interconnection networks is a critical aspect that significantly impacts system performance and functionality. When quantifying the reliability of these networks, extra connectivity and extra diagnosability serve as fundamental metric parameters, offering valuable insights into the network’s resilience and fault-handling capabilities. In this paper, we investigate the 1-extra connectivity and 1-extra diagnosability of the <i>n</i>-dimensional enhanced folded hypercube-like network. Through analysis, we show that the 1-extra connectivity of this network is <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>2</mn></mrow></semantics></math></inline-formula>. Moreover, for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mo>></mo><mn>5</mn></mrow></semantics></math></inline-formula>, we determine its 1-extra diagnosability under both the PMC model and the MM<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mo></mo><mo>∗</mo></msup></semantics></math></inline-formula> model to be <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>2</mn><mi>n</mi><mo>+</mo><mn>3</mn></mrow></semantics></math></inline-formula>. These results show that as the dimension <i>n</i> increases, both the 1-extra connectivity and 1-extra diagnosability of the network approach approximately twice the value of traditional diagnosability metrics. This provides quantitative insights into the reliability properties of the enhanced folded hypercube-like network, contributing to a better understanding of its performance in terms of connectivity and fault diagnosis.https://www.mdpi.com/2227-7390/13/15/2441connectivitydiagnosabilityenhanced folded hypercube-like networks |
| spellingShingle | Yihong Wang Cheng-Kuan Lin Extra Connectivity and Extra Diagnosability of Enhanced Folded Hypercube-like Networks Mathematics connectivity diagnosability enhanced folded hypercube-like networks |
| title | Extra Connectivity and Extra Diagnosability of Enhanced Folded Hypercube-like Networks |
| title_full | Extra Connectivity and Extra Diagnosability of Enhanced Folded Hypercube-like Networks |
| title_fullStr | Extra Connectivity and Extra Diagnosability of Enhanced Folded Hypercube-like Networks |
| title_full_unstemmed | Extra Connectivity and Extra Diagnosability of Enhanced Folded Hypercube-like Networks |
| title_short | Extra Connectivity and Extra Diagnosability of Enhanced Folded Hypercube-like Networks |
| title_sort | extra connectivity and extra diagnosability of enhanced folded hypercube like networks |
| topic | connectivity diagnosability enhanced folded hypercube-like networks |
| url | https://www.mdpi.com/2227-7390/13/15/2441 |
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