Construction of Four Completely Independent Spanning Trees on Augmented Cubes
Combinatorics
2017-05-04 v1
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.
Keywords
Cite
@article{arxiv.1705.01358,
title = {Construction of Four Completely Independent Spanning Trees on Augmented Cubes},
author = {S. A. Mane and S. A. Kandekar and B. N. Waphare},
journal= {arXiv preprint arXiv:1705.01358},
year = {2017}
}