Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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EXPONENTS OF CARTESIAN PRODUCTS OF TWO DIGRAPHS OF SPECIAL ORDERS

  • Kim, Byeong-Moon (DEPARTMENTS OF MATHEMATICS GANGNEUAND-WONJU NATIONAL UNIVERSITY) ;
  • Rho, Yoo-Mi (DEPARTMENTS OF MATHEMATICS UNIVERSITY OF INCHEON)
  • Received : 2009.01.13
  • Published : 2010.11.30
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Abstract

In this paper, we find the maximum exponent of D ${\times}$ E, the cartesian product of two digraphs D and E on n, n + 2 vertices, respectively for an even integer $n\geq4$. We also characterize the extrema cases.

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References

  1. A. Brauer, On a problem of partitions, Amer. J. Math. 64 (1942), 299-312. https://doi.org/10.2307/2371684
  2. B. M. Kim, B. C. Song, and W. Hwang, Wielandt type theorem for Cartesian product of digraphs, Linear Algebra Appl. 429 (2008), no. 4, 841-848. https://doi.org/10.1016/j.laa.2008.04.029
  3. R. Lamprey and B. Barnes, Primitivity of products of digraphs, Proceedings of the Tenth Southeastern Conference on Combinatorics, Graph Theory and Computing (Florida Atlantic Univ., Boca Raton, Fla., 1979), pp. 637-644, Congress. Numer., XXIII-XXIV, Utilitas Math., Winnipeg, Man., 1979.
  4. B. L. Liu, B. D. McKay, N. C. Wormald, and K. Zhang, The exponent set of symmetric primitive (0; 1) matrices with zero trace, Linear Algebra Appl. 133 (1990), 121-131. https://doi.org/10.1016/0024-3795(90)90244-7
  5. J. B. Roberts, Note on linear forms, Proc. Amer. Math. Soc. 7 (1956), 465-469. https://doi.org/10.1090/S0002-9939-1956-0091961-5
  6. J. Y. Shao, The exponent set of symmetric primitive matrices, Sci. Sinica Ser. A 9 (1986), 931-939.
  7. H. Wielandt, Unzerlegbare, nicht negative Matrizen, Math. Z. 52 (1950), 642-648. https://doi.org/10.1007/BF02230720