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 Total dominations in $P_{6}$-free graphs Commun. Korean Math. Soc. 2013 Vol. 28, No. 4, 857-863 https://doi.org/10.4134/CKMS.2013.28.4.857Printed October 1, 2013 Xue-gang Chen and Moo Young Sohn North China Electric Power University, Changwon National University Abstract : 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. Keywords : total domination numbers, $P_6$-free graphs Downloads: Full-text PDF