雙扭超方體之容錯泛圈性質

Abstract

雙扭超方體(twisted cube)是由Hilbers 等人利用特定的規則來改變超立方體(hypercube)原有連結所得到。近年來已經有不少有關雙扭超方體的研究，在這篇論文裡，我們將利用已知雙扭超方體的容錯漢米爾頓性質、容錯漢米爾頓連結性質，和泛圈性質，來證明一個n階層的雙扭超方體，即使是壞了n-2個點(node)或邊(edge)依然保有泛圈性質，而且這個結果是最佳的.

The Twisted cube, first proposed by Hilbers et al., is derived by changing some connection of hypercube, according to specific rules. In recent years, many topological properties of this variation have been studied, it has been proven that it is a pancyclic network.. Besides, Huang et al. also showed that a n-dimentional twisted cubeis is (n-2) fault-tolerant hamiltonian and (n-3) fault-tolerant hamiltonian connected. According to these properties, in this paper, we will prove that a n-dimentional twisted cube is a (n-2) fault-tolerant pancyclic network.