Independent spanning trees in crossed cubes

  • Authors:

  • Baolei Cheng;Jianxi Fan;Xiaohua Jia;Shukui Zhang

  • Affiliations:

  • School of Computer Science and Technology, Soochow University, Suzhou 215006, China and Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, China;School of Computer Science and Technology, Soochow University, Suzhou 215006, China;Department of Computer Science, City University of Hong Kong, Hong Kong;School of Computer Science and Technology, Soochow University, Suzhou 215006, China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2013

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Abstract

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 CQ"n 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 CQ"n(n=1). Then, we propose an O(Nlog^2N) constructive algorithm, where N=2^n is the number of vertices in CQ"n.