Constructive Algorithm of Independent Spanning Trees on Moebius Cubes

摘要

Independent spanning trees (ISTs) on networks have applications in networks such as reliable communication protocols, the multi-node broadcasting, one-to-all broadcasting, reliable broadcasting and secure message distribution. However, there is a problem on ISTs on graphs: If a graph G is n -connected (n ≥ 1), then there are n ISTs rooted at an arbitrary vertex on G. This problem has remained open for n ≥ 5. In this paper, we consider the construction of ISTs on Mobius cubes-a class of hypercube variants. An O(N log N) recursive algorithm is proposed to construct n ISTs rooted at an arbitrary vertex on the n-dimensional Mobius cube M_n, where N = 2" is the number of vertices in M_n. Furthermore, we prove that each 1ST obtained by our algorithm is isomorphic to an n-level binomial-like tree with the height n + 1 for n ≥ 2.