One-to-many node-disjoint paths of hyper-star networks

In practice, it is important to construct node-disjoint paths in networks, because they can be used to increase the transmission rate and enhance the transmission reliability. The hyper-star networks HS(2n,n) were introduced to be a competitive model for both the hypercubes and the star graphs. In this paper, one-to-many node-disjoint paths are constructed between a fixed node and nn other nodes of HS(2n,n) such that each of these paths has length at most 4 more than the shortest path to that node. Moreover, their maximum length is not greater than the diameter+2.