East Asian mathematical journal

  • 제26권3호
  • /
  • Pages.423-427
  • /
  • 2010
  • /
  • 1226-6973(pISSN)
  • /
  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

DOMINATIONS ON BIPARTITE STEINHAUS GRAPHS

  • 투고 : 2010.01.19
  • 심사 : 2010.04.27
  • 발행 : 2010.05.31
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper, we give an upper bound for dominations of Steinhaus graphs, and the domination numbers of the bipartite Steinhaus graphs. Also, we give an upper bound for Nordhaus-Gaddum type result for the bipartite Steinhaus graphs.

키워드

참고문헌

  1. B. Bollobas, Graph Theory, Springer-Verlag, New York, 1979.
  2. W. M. Dymacek, Bipartite Steinhaus graphs, Discrete Mathematics 59 (1986), 9-22. https://doi.org/10.1016/0012-365X(86)90064-6
  3. W. M. Dymacek and T. Whaley, Generating strings for bipartite Steinhaus graphs, Discrete Mathematics 141 (1995), no1-3, 95-107. https://doi.org/10.1016/0012-365X(93)E0211-L
  4. W. M. Dymacek, M. Koerlin and T. Whaley, A survey of Steinhaus graphs, Proceedings of the Eighth Quadrennial International Conference on Graph Theory, Combinatorics, Algorithm and Applications, 313-323, Vol. 1, 1998.
  5. G. J. Chang, B. DasGupta, W. M. Dymacek, M. Furer, M. Koerlin, Y. Lee and T. Wha- ley, Characterizations of bipartite Steinhaus graphs, Discrete Mathematics 199 (1999), 11-25. https://doi.org/10.1016/S0012-365X(98)00282-9
  6. H. Harborth, Solution of Steinhaus's problem with plus and minus signs, J. Combina- torial Theory 12(A) (1972), 253-259. https://doi.org/10.1016/0097-3165(72)90039-8
  7. T. W. Haynes, S. T. Hedetniemi and P. J. Slater, Fundamentals of Domination in Graphs, Marcel Dekker, New York, 1998.
  8. D. Lim, Upper bound on domination number of Steinhaus graphs, J. Inst. Nat. Sci. Vol.12, No.2 (2007), 9-14.
  9. R. Stanley, Enumerative Combinatorics Vol. I, Wadsworth and Brooks/Cole, Monterey, 1986.