The connectivity and nature diagnosability of expanded $k$-ary $n$-cubes

Wang, Mujiangshan; Lin, Yuqing; Wang, Shiying

doi:10.1051/ita/2017008

The connectivity and nature diagnosability of expanded

k

-ary

n

-cubes

Wang, Mujiangshan ¹ ; Lin, Yuqing ¹ ; Wang, Shiying ²

¹ School of Electrical Engineering and Computer Science, The University of Newcastle NSW 2308, Australia.
² School of Mathematics and Information Science, Henan Normal University, Xinxiang, Henan 453007, PR China.

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 51 (2017) no. 2, pp. 71-89.

Résumé

Connectivity and Diagnosability play an important role in measuring the fault tolerance of interconnection networks. As a topology structure of interconnection networks, the expanded $k$ -ary $n$ -cube $X Q^{k}$ $_{n}$ has many good properties. In this paper, we prove that (1) the connectivity of $X Q^{k}$ $_{n}$ is $4 n$ ; (2) the nature connectivity of $X Q^{k}$ $_{n}$ is $8 n - 4$ ; (3) the nature diagnosability of $X Q^{k}$ $_{n}$ under the PMC model and MM $^{*}$ model is $8 n - 3$ for $n \geq 2$ .

MR Zbl

DOI : 10.1051/ita/2017008

Classification : 05C25, 05C90
Mots-clés : Interconnection networks, Combinatorics, Connectivity, Diagnosability, Expandedk-aryn-cubes

Affiliations des auteurs :

Wang, Mujiangshan ¹ ; Lin, Yuqing ¹ ; Wang, Shiying ²

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     author = {Wang, Mujiangshan and Lin, Yuqing and Wang, Shiying},
     title = {The connectivity and nature diagnosability of expanded $k$-ary $n$-cubes},
     journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
     pages = {71--89},
     publisher = {EDP-Sciences},
     volume = {51},
     number = {2},
     year = {2017},
     doi = {10.1051/ita/2017008},
     mrnumber = {3731538},
     zbl = {1379.05056},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ita/2017008/}
}

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Wang, Mujiangshan; Lin, Yuqing; Wang, Shiying. The connectivity and nature diagnosability of expanded $k$-ary $n$-cubes. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 51 (2017) no. 2, pp. 71-89. doi : 10.1051/ita/2017008. https://www.numdam.org/articles/10.1051/ita/2017008/

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