带有条件故障边的3元n方体的圈嵌入

Embedding Cycles in 3 Ary n Cubes with Conditional Edge Faults

研究了带有条件故障边的3元n方体的圈嵌入问题,证明了对于n≥2的3元n方体,其每个顶点至少与两条非故障边相关联.当它的故障边不超过2n-1且由这些故障边导出的子图不含圈时,该3元n方体存在不含故障边的长度在3到3n间的任意长的圈.

The cycle embedding problem in 3 ary n cubes with conditional fault edges was discussed.It is proved that each vertex is incident to at least two healthy edges for those cubes of n≥2 and there exists a cycle with its length from 3 to 3n in a 3 ary n cube if the number of fault edges are less than 2n-1 and the subgraph induced by the fault edges is acyclic.