Improving the Height of Independent Spanning Trees on Folded Hyper-Stars∗

Hypercubes and star graphs are widespread topologies of interconnection networks. The class of hyper-stars was introduced as a new type of interconnection network to compete with both hypercubes and star graphs, and the class of folded hyper-stars is a strengthened variation of hyperstars with additional links to connect nodes with complemented 0/1-strings. Constructing independent spanning trees (ISTs) has numerous applications in networks such as fault-tolerant broadcasting and secure message distribution. Recently, Yang and Chang [33] proposed an algorithm to construct k+ 1 ISTs on folded hyper-star FHS(2k, k). For k > 4, their construction includes k ISTs with the height 2k−2 and the other one with the height k + 1. In this paper, we refine their constructing rules on FHS(2k, k) for k > 3 and provide a set of construction including k ISTs with the height k+2 and the other one with the height k + 1. As a byproduct, we obtain an improvement on the upper bound of the fault diameter (respectively, the wide diameter) of FHS(2k, k). Keyword: folded hyper-stars; independent spanning trees; interconnection networks; fault-tolerant broadcasting; secure message distribution.