The generalized measure of edge fault tolerance in exchanged 3-ary n-cube. Issue 3 (4th May 2023) - Yang, Yayu; Zhang, Mingzu; Meng, Jixiang
Abstract : The exchanged 3-ary n -cube E 3 C ( 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 λ h ( G ) is the minimum cardinality of all h -edge-cuts of G . For 1 ≤ r ≤ s ≤ t and 0 ≤ h ≤ r, in this paper, we determine the 2 h -edge-connectivity of exchanged 3-ary n -cubes, E 3 C ( r, s, t ), and prove the exact values λ 2 h ( E 3 C ( r, s, t ) ) = 2 ⋅ 3 h ( r + 1 − h ) . GRAPHICAL ABSTRACT: UF0001