边故障5元n立方体的两条不交覆盖路

2-Disjoint Path Covers in 5-ary n-cubes with Fault Edges

研究具有故障边的5元n立方体的两条不交路覆盖问题。用归纳假设法证明了:若Q5n的边故障集F中至多有2n-4条边,对于Q5n中任意四个顶点a,b,c,d,则Q5n-F存在两条顶点不交的覆盖路P1和P2,这里P1连接a和b,P2连接c和d.

The paper studies the problem of 2-disjoint paths cover of 5-ary n-cube. Let F be any subset of edges with ｜F｜≤2n-4, the following result is obtained. Assuming that a,b,c and d are arbitrarily four distinct vertices in Qn5,there exist two fault-free vertex-disjoint paths P1 between a and b and P2 between c and in d such that cover of Qn5.