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

The exchanged 3-ary n-cube , proposed by Lv et al. in 2021, is obtained by removing edges from a 3-ary n-cube , 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 is the minimum cardinality of all h-edge-cuts of G. For and , in this paper, we determine the -edge-connectivity of exchanged 3-ary n-cubes, , and prove the exact values . GRAPHICAL ABSTRACT