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Independent spanning trees of product graphs

  • Koji Obokata
  • Yukihiro Iwasaki
  • Feng Bao
  • Yoshihide Igarashi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1197)

Abstract

A graph G is called an n-channel graph at vertex r if there are n independent spanning trees rooted at r. A graph G is called an n-channel graph if for every vertex u, G is an n-channel graph at u. Independent spanning trees of a graph play an important role in faulttolerant broadcasting in the graph. In this paper we show that if G1 is an n1-channel graph and G2 is an n2-channel graph, then G1×G2 is an (n1+n2)-channel graph. We prove this fact by a construction of n1+n2 independent spanning trees of G1 × G2 from n1 independent spanning trees of G1 and n2 independent spanning trees of G2.

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References

  1. 1.
    F. Bao, Y. Igarashi, K. Katano: Broadcasting in hypercubes with randomly distributed Byzantine faults. 9th International Workshop on Distributed Algorithms Le Mont-Saint-Michel LNCS 972 (1995) 215–229Google Scholar
  2. 2.
    F. Bao, Y. Igarashi, S. R. öhring: Reliable broadcasting in product networks. IEICE Technical Report COMP 95-18 (1995) 57–66Google Scholar
  3. 3.
    J. Cheriyan, S. N. Maheshwari: Finding nonseparating induced cycles and independent spanning trees in 3-connected graphs. J. Algorithms 9 (1988) 507–537Google Scholar
  4. 4.
    A. Itai, M. Rodeh: The multi-tree approach to reliability in distributed networks. Information and Computation 79 (1988) 43–59Google Scholar
  5. 5.
    S. Khuller, B. Schieber: On independent spanning trees. Information Processing Letters 42 (1992) 321–323Google Scholar
  6. 6.
    A. Youssef: Cartesian product networks. The 1991 International Conference on Parallel Processing I (1991) 684–685Google Scholar
  7. 7.
    A. Zehavi, A. Itai: Three tree-paths. J. Graph Theory 13 (1989) 175–188Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Koji Obokata
    • 1
  • Yukihiro Iwasaki
    • 1
  • Feng Bao
    • 1
  • Yoshihide Igarashi
    • 1
  1. 1.Department of Computer ScienceGunma UniversityKiryuJapan

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