Constructing Two Completely Independent Spanning Trees in Balanced Hypercubes

A set of spanning trees of a graphsG are called completely independent spanning trees (CISTs for short) if for every pair of vertices x, y is an element of V(G), the paths joining x and y in any two trees have neither vertex nor edge in common, except x and y. Constructing CISTs has applications on interconnection networks such as fault-tolerant routing and secure message transmission. In this paper, we investigate the problem of constructing two CISTs in the balanced hypercube BHn, which is a hypercube-variant network and is superior to hypercube due to having a smaller diameter. As a result, the diameter of CISTs we constructed equals to 9 for BH2 and 6n - 2 for BHn when n >= 3.