An algorithm to construct independent spanning trees on parity cubes

Independent spanning trees have applications in networks such as reliable communication protocols, one-to-all broadcasting, reliable broadcasting, and secure message distribution. Thus, the designs of independent spanning trees in several classes of networks have been widely investigated. However, there is a conjecture on independent spanning trees: any n-connected graph has n independent spanning trees rooted at an arbitrary vertex. This conjecture still remains open for n >= 5. In this paper, by proposing an algorithm to construct n independent spanning trees rooted at any vertex, we confirm the conjecture on n-dimensional parity cube PQ(n) - a variant of n-dimensional hypercube. Furthermore, we prove that all independent spanning trees rooted at an arbitrary vertex constructed by our construction method are isomorphic and the height of each tree is n + 1 for any integer it >= 2. (c) 2012 Elsevier B.V. All rights reserved.