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

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)(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 2h-edge-connectivity of exchanged 3-ary n-cubes, E3C(r, s, t), and prove the exact values lambda(2h)(E3C(r, s, t)) = 2 middot 3(h)(r + 1 - h).