Korean Journal of Mathematics

  • 제23권1호
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  • Pages.29-36
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  • 2015
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  • 1976-8605(pISSN)
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  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
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BASE OF THE NON-POWERFUL SIGNED TOURNAMENT

  • 투고 : 2014.11.05
  • 심사 : 2015.01.23
  • 발행 : 2015.03.30
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초록

A signed digraph S is the digraph D by assigning signs 1 or -1 to each arc of D. The base of S is the minimum number k such that there is a pair walks which have the same initial and terminal point with length k, but different signs. In this paper we show that for $n{\geq}5$ the upper bound of the base of a primitive non-powerful signed tournament Sn, which is the signed digraph by assigning 1 or -1 to each arc of a primitive tournament $T_n$, is max{2n + 2, n+11}. Moreover we show that it is extremal except when n = 5, 7.

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참고문헌

  1. V. K. Balakrishnan, Graph theory, McGraw-Hill,N.Y., 1997.
  2. Y. Gao, Y. Huang and Y. Shao, Bases of primitive non-powerful signed symmetric digraphs with loops, Ars. Combinatoria 90 (2009), 383-388.
  3. B. Li, F. Hall and J. Stuart, Irreducible powerful ray pattern matrices, Linear Algebra and Its Appl., 342 (2002), 47-58. https://doi.org/10.1016/S0024-3795(01)00436-0
  4. Q. Li and B. Liu, Bounds on the kth multi-g base index of nearly reducible sign pattern matrices, Discrete Math. 308 (2008), 4846-4860. https://doi.org/10.1016/j.disc.2007.09.004
  5. J. Moon and N, Pullman, On the powers of tournament matrices, J. Comb. Theory 3 (1967), 1-9. https://doi.org/10.1016/S0021-9800(67)80009-7
  6. Y. Shao and Y. Gao, The local bases of non-powerful signed symmetric digraphs with loops, Ars. Combinatoria 90 (2009), 357-369.
  7. B. Song and B. Kim, The bases of primitive non-powerful complete signed graphs, Korean J. Math. 22 (2014), 491-500. https://doi.org/10.11568/kjm.2014.22.3.491
  8. L. You, J. Shao and H. Shan, Bounds on the bases of irreducible generalized sign pattern matrices, Linear Algebra and Its Appl. 427 (2007), 285-300. https://doi.org/10.1016/j.laa.2007.07.019