Vertex-disjoint paths in a 3-ary \(n\)-cube with faulty vertices (Q2196925)

Summary: The construction of vertex-disjoint paths (disjoint paths) is an important research topic in various kinds of interconnection networks, which can improve the transmission rate and reliability. The \(k\)-ary \(n\)-cube is a family of popular networks. In this paper, we determine that there are \(m\) (\( 2 \leq m \leq n\)) disjoint paths in 3-ary \(n\)-cube covering \(Q_n^3-F\) from \(S\) to \(T\) (many-to-many) with \(\left| F\right|\leq2n-2m\) and from \(s\) to \(T\) (one-to-many) with \(\left| F\right|\leq2n-m-1\) where \(s\) is in a fault-free cycle of length three.