대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제28권4호
  • /
  • Pages.857-863
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  • 2013
  • /
  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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TOTAL DOMINATIONS IN P6-FREE GRAPHS

  • Chen, Xue-Gang (Department of Mathematics North China Electric Power University) ;
  • Sohn, Moo Young (Department of Mathematics Changwon National University)
  • 투고 : 2012.12.24
  • 발행 : 2013.10.31
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초록

In this paper, we prove that the total domination number of a $P_6$-free graph of order $n{\geq}3$ and minimum degree at least one which is not the cycle of length 6 is at most $\frac{n+1}{2}$, and the bound is sharp.

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과제정보

연구 과제 주관 기관 : Changwon National University

참고문헌

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  5. O. Favaron and M. A. Henning, Total domination in claw-free graphs with minimum degree 2, Discrete Math. 308 (2008), no. 15, 3213-3219. https://doi.org/10.1016/j.disc.2007.06.024
  6. O. Favaron, M. A. Henning, C. M. Mynhart, and J. Puech, Total domination in graphs with minimum degree three, J. Graph Theory 34 (2000), no. 1, 9-19. https://doi.org/10.1002/(SICI)1097-0118(200005)34:1<9::AID-JGT2>3.0.CO;2-O
  7. M. A. Henning, Graphs with large total domination number, J. Graph Theory 35 (2000), no. 1, 21-45. https://doi.org/10.1002/1097-0118(200009)35:1<21::AID-JGT3>3.0.CO;2-F