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Total dominations in P6-free graphs

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In this paper, we prove that the total domination number ofa P6-free graph of order n≥ 3 and minimum degree at least one which isnot the cycle of length 6 is at most n+1 2, and the bound is sharp.

Abstract

In this paper, we prove that the total domination number ofa P6-free graph of order n≥ 3 and minimum degree at least one which isnot the cycle of length 6 is at most n+1 2, and the bound is sharp.

참고문헌 (7)

  1. D. Archdeacon, "Some remarks on domination", J. Graph Theory, 46(3), pp.207~210 (2004)
  2. R. C. Brigham, "Connected graphs with maximum total domination number", J. Combin. Math. Combin. Comput, 34, pp.81~95 (2000)
  3. E. J. Cockayne, "Total domination in graphs", Net- works, 10(3), pp.211~219 (1980)
  4. P. Dorbec, "Paired-domination in P5-free graphs", Graphs Combin, 24(4), pp.303~308 (2008)
  5. O. Favaron, "Total domination in claw-free graphs with minimum degree 2", Discrete Math, 308(15), pp.3213~3219 (2008)
  6. O. Favaron, "Total domination in graphs with minimum degree three", J. Graph Theory, 34(1), pp.9~19 (2000)
  7. M. A. Henning, "Graphs with large total domination number", J. Graph Theory, 35(1), pp.21~45 (2000)

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