Construction of Four Completely Independent Spanning Trees on Augmented Cubes

Abstract

Let T1, T2, ......., T k be spanning trees in a graph G. If for any pair of vertices {u, v} of G, the paths between u and v in every Ti( 1 ≤ i ≤ k) do not contain common edges and common vertices, except the vertices u and v, then T1, T2, ......., T k are called completely independent spanning trees in G. The n−dimensional augmented cube, denoted as AQn, a variation of the hypercube possesses several embeddable properties that the hypercube and its variations do not possess. For AQn (n ≥ 6), construction of 4 completely independent spanning trees of which two trees with diameters 2n − 5 and two trees with diameters 2n − 3 are given.