点故障3-ary n立方体中两条无故障点不交路

Two Fault-free Vertex-disjoint Paths in 3-ary n-cube with Faulty Vertices

研究了含有故障点的Q3n中两条顶点不交的无故障路问题,得到以下结论:当n≥2,设FV(Q3n),若|F|≤2n-4,令x1,y1,x2,y2是Q3n-F中任意四个顶点,则在Q3n-F中存在两条顶点不交的路P1和P2,使得V(P1)∪V(P2)=V(Q3n-F),这里P1连接x1和y1,P2连接x2和y2.

In this paper, the following result was obtained. Let Q3n be a 3 - ary n - cube, where n ≥2 , and F be any subset of vertices with ｜ F｜≤2n - 4. Assume that x1 ,x2 ,y1 and y2 are any four distinct vertices in Q3 , then there exist two fault - free vertex - disjoint paths P1 between x1 and y1 and P2 between x2 and y2 such that V（P1） ∪ V（P2） = V（Qn-F）.