Constructing independent spanning trees for locally twisted cubes

Abstract

The independent spanning trees (ISTs) problem attempts to construct a set of pairwise independent spanning trees and it has numerous applications in networks such as data broadcasting, scattering and reliable communication protocols. The well-known ISTs conjecture, Vertex/Edge Conjecture, states that any n-connected/n-edge-connected graph has n vertex-ISTs/edge-ISTs rooted at an arbitrary vertex r. It has been shown that the Vertex Conjecture implies the Edge Conjecture. In this paper, we consider the independent spanning trees problem on the n-dimensional locally twisted cube LTQ(n). The very recent algorithm proposed by Hsieh and Tu (2009) [12] is designed to construct n edge-ISTs rooted at vertex 0 for LTQ(n). However, we find out that LTQ(n) is not vertex-transitive when n >= 4; therefore Hsieh and Tu's result does not solve the Edge Conjecture for LTQ(n),,. In this paper, we propose an algorithm for constructing n vertex-ISTs for LTQ(n); consequently, we confirm the Vertex Conjecture (and hence also the Edge Conjecture) for LTQ(n),. (C) 2011 Elsevier B.V. All rights reserved.