Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2013; 28(4): 857-863

Printed October 1, 2013

https://doi.org/10.4134/CKMS.2013.28.4.857

Copyright © The Korean Mathematical Society.

Total dominations in $P_{6}$-free graphs

Xue-gang Chen and Moo Young Sohn

North China Electric Power University, Changwon National University

Abstract

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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

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