Independent spanning trees in crossed cubes
Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review
Related Research Unit(s)
|Journal / Publication||Information Sciences|
|Publication status||Published - 1 Jun 2013|
|Link to Scopus||https://www.scopus.com/record/display.uri?eid=2-s2.0-84875214715&origin=recordpage|
Multiple independent spanning trees (ISTs) can be used for data broadcasting in networks, which can provide advantageous performances, such as the enhancement of fault-tolerance, bandwidth, and security. However, there is a conjecture on the existence of ISTs in graphs: If a graph G is n-connected (n ≥ 1), then there are n ISTs rooted at an arbitrary vertex in G. This conjecture has remained open for n ≥ 5. The n-dimensional crossed cube CQn is a n-connected graph with various desirable properties, which is an important variant of the n-dimensional hypercube. In this paper, we study the existence and construction of ISTs in crossed cubes. We first give a proof of the existence of n ISTs rooted at an arbitrary vertex in CQn(n ≥ 1). Then, we propose an O(N log2N) constructive algorithm, where N = 2n is the number of vertices in CQn. © 2013 Elsevier Inc. All rights reserved.
- Crossed cube, Fault-tolerant broadcasting, Independent spanning trees, Internally vertex-disjoint paths