An algorithm to construct independent spanning trees on parity cubes

  • Authors:

  • Yan Wang;Jianxi Fan;Xiaohua Jia;He Huang

  • Affiliations:

  • School of Computer Science and Technology, Soochow University, Suzhou 215006, China and Provincial Key Laboratory for Computer Information Processing Technology, Soochow University, Suzhou 215006, ...;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:
  • Theoretical Computer Science
  • Year:
  • 2012

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Abstract

Independent spanning trees have applications in networks such as reliable communication protocols, one-to-all broadcasting, reliable broadcasting, and secure message distribution. Thus, the designs of independent spanning trees in several classes of networks have been widely investigated. However, there is a conjecture on independent spanning trees: any n-connected graph has n independent spanning trees rooted at an arbitrary vertex. This conjecture still remains open for n=5. In this paper, by proposing an algorithm to construct n independent spanning trees rooted at any vertex, we confirm the conjecture on n-dimensional parity cube PQ"n -- a variant of n-dimensional hypercube. Furthermore, we prove that all independent spanning trees rooted at an arbitrary vertex constructed by our construction method are isomorphic and the height of each tree is n+1 for any integer n=2.