变形超立方体的圈和路嵌入(英文)

Cycles and paths embedded in varietal hypercubes

作为超立方体网络Qn的变形,n维变形超立方体VQn具有许多优于超立方体所具有的性质.这里证明了对任何整数l∈[4,2n],VQn中每条边被包含在长度为l的圈中除非l=5;对任何顶点对(x,y)和整数l∈[d,2n-1],其中,d为这两点之间的距离,VQn中存在长度为l的xy路除非当d=1时l=2,4.

The varietal hypercube VQn is a variant of the hypercube Qn and has better properties than Qn with the same number of edges and vertices .It was proved that every edge of VQn is contained in cycles of every length from 4 to 2 n except 5 ,and that every pair of vertices with distance d is connected by paths of every length from d to 2 n - 1 except 2 and 4 if d = 1 .