广义超立方体的广义连通度

Generalized Connectivity of Generalized Hypercubes

k元n方体是著名的超立方体网络的推广。针对k元n方体的广义3-连通度问题,证明了对任意的整数k≥3和n≥1,k元n方体中存在2n-1棵内部不交的连接任意3个顶点的树。

The k-ary n-cube is a generalization of the famous hypercube network. Aiming at the problem of the generalized 3-connectivity of the k-ary n-cube,it was proved that for any integers k≥3 and n≥1,there exist 2n-1 internally disjoint trees connecting any three vertices in the k-ary n-cube.