Fault-Tolerant Cycle Embedding into 3-Ary n-Cubes with Structure Faults
Weibei Fan, Yan Wang, Jing Sun, Zhijie Han, Peng Li, Ruchuan Wang · 2019
3-Ary n-cube network, denoted by Q3 r, as the most important network topology in interconnection networks. It has been widely used because of its regular topology, low degree of nodes and easy implementation on a single chip. We study the cycle embedding into Q3 rwith structure faults, where each fault component is isomorphic to any connected subgraph of H1,3. Let M be a connected graph with M ϵ{W1,W1,1,W1,2,W1,3}. We prove that there is an arbitrary length cycle from 3 to |V (Q3/r - W)| if the faulty component is no more than r-1 and every fault component is isomorphic to any connected subgraph M, where W is the faulty components in an n-dimensional 3-ary n-cube. It is the first work which takes structure faults into account to study fault-tolerant pancyclicity of interconnection networks.