• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.857-863
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• 2013

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.