# Constructing edge-disjoint spanning trees in augmented cubes

## TL;DR

This paper presents a method for constructing the maximum possible number of edge-disjoint spanning trees in augmented cubes, which are a variation of hypercubes with superior properties, enhancing reliable communication protocols.

## Contribution

It provides an optimal construction of n-1 edge-disjoint spanning trees in n-dimensional augmented cubes, improving upon previous results for hypercube variants.

## Key findings

- Constructed n-1 edge-disjoint spanning trees in AQn for n > 2
- Proved the construction is optimal with respect to the number of trees
- Enhanced reliability in communication protocols using these trees

## Abstract

Let T1, T2,.... Tk be spanning trees in a graph G. If for any pair of vertices u and v of G, the paths between u and v in every Ti( 0 < i < k+1) do not contain common edges then T1, T2,.... Tk are called edge-disjoint spanning trees in G. The design of multiple edge-disjoint spanning trees has applications to the reliable communication protocols. The n-dimensional augmented cube, denoted as AQn, a variation of the hypercube, possesses some properties superior to those of the hypercube. For AQn (n > 2), construction of n-1 edge-disjoint spanning trees is given the result is optimal with respect to the number of edge-disjoint spanning trees.