The generalized measure of edge fault tolerance in exchanged 3-ary n-cube

Abstract

The exchanged 3-ary n-cube $E3C(r,s,t)$, proposed by Lv et al. in 2021, is obtained by removing edges from a 3-ary n-cube $Q_n^3$, where r + s + t + 1 = n. The topological interconnection network of a multiprocessor system can be modeled as a connected graph. Analyzing the fault tolerance of its topological structure is critical in the course of design and maintenance of it. Given a connected graph G, let F be an edge subset of G. F is called an h-edge-cut of G, if G−F is disconnected and each remaining component has the minimum degree of at least h. The h-edge-connectivity ${\lambda }^h\left(G\right)$ is the minimum cardinality of all h-edge-cuts of G. For $1\le r\le s\le t$ and $0\le h\le r$, in this paper, we determine the $2h$-edge-connectivity of exchanged 3-ary n-cubes, $E3C(r,s,t)$, and prove the exact values ${\lambda }^{2h}\left(E3C\right(r,s,t\left)\right)=2\cdot 3^h(r+1-h)$.

GRAPHICAL ABSTRACT

Keywords:

• Interconnection networks
• fault tolerance
• h-edge-connectivity
• exchanged 3-ary n-cube

Acknowledgments

The authors would like to thank anonymous referees and editors for their help. Their valuable comments and suggestions help to improve the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Natural Science Foundation of Xinjiang (No. 2020D04046), the National Natural Science Foundation of China (No. 12101528), the Science and Technology Project of Xinjiang Uygur Autonomous Region (2020D01C069), and the Doctoral Startup Foundation of Xinjiang University (No. 62031224736).