Towards the Independent Spanning Trees in the Line Graphs of Interconnection Networks

Abstract

Node/edge-Independent spanning trees (ISTs) have attracted a lot of attention in the past twenty years. Many results such as edge-disjoint Hamilton cycles, traceability, number of spanning trees, structural properties, topological indices, etc, have been obtained on line graphs, and researchers have applied the line graphs of some interconnection networks into data center networks, such as SWCube, BCDC, etc. However, node/edge conjecture is still open for n-node-connected interconnection network with \(n\ge \) 5. So far, results have been obtained on a lot of special interconnection networks, but few results are reported on the line graphs of them. In this paper, we consider the problem of constructing node-ISTs in a line graph G of an interconnection network \(G'\). We first give the construction of node-ISTs in \(G'\) based on the edge-ISTs in G. Then, an algorithm to construct node-ISTs in G based on the edge-ISTs in \(G'\) is presented. At the end, simulation experiments on the line graphs of hypercubes show that the maximal height of the constructed node-ISTs on the line graph of n-dimensional hypercube is \(n+1\) for \(n\ge 3\).