Construction of Four Completely Independent Spanning Trees on Augmented Cubes

TL;DR

This paper constructs four completely independent spanning trees in augmented cubes, with specific diameter properties, enhancing understanding of fault-tolerant network structures in these complex graphs.

Contribution

It presents a novel construction of four independent spanning trees in augmented cubes, including diameter specifications, advancing network reliability research.

Findings

Constructed four independent spanning trees in AQn for n > 5.

Two trees have diameter 2n - 5, and two have diameter 2n - 3.

Enhances fault-tolerance analysis in augmented cube networks.

Abstract

Let T1, T2,..., Tk 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( 0 < i < k+1) do not contain common edges and common vertices, except the vertices u and v, then T1, T2,..., Tk 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 > 5), construction of 4 completely independent spanning trees of which two trees with diameters 2n - 5 and two trees with diameters 2n - 3 are given.