The Conditional Connectivity of Möbius Cubes under the 1-Safe Condition

Studying the properties of an interconnection network is an important part of the study of any parallel processing or distributed system. The hypercube network is widely used as architecture for parallel machines. As a hypercube variant, the Möbius cube has many attractive properties. This paper studied the conditional connectivity of Möbius cube under the 1-safe condition. Through some preliminaries, it was proved that there are at least 2n-2 node-disjoint paths between any two nodes in Möbius cube. Based on this, we further proved that the conditional connectivity of Möbius cube under the 1-safe condition is 2n-2, which shows the fault tolerance of the Möbius cube network topology is better.