On minus total domination of directed graphs
Commun. Korean Math. Soc. 2014 Vol. 29, No. 2, 359-366
https://doi.org/10.4134/CKMS.2014.29.2.359
Printed April 1, 2014
WenSheng Li, Huaming Xing, and Moo Young Sohn
Langfang Normal College, Tianjin University of Science & Technology, Changwon National University
Abstract : A three-valued function $f$ defined on the vertices of a digraph $D=(V, A)$, $f:V\rightarrow\{-1,0,+1\}$ is a minus total dominating function(MTDF) if $f(N^-(v))\geq 1$ for each vertex $v\in V$. The minus total domination number of a digraph $D$ equals the minimum weight of an MTDF of $D$. In this paper, we discuss some properties of the minus total domination number and obtain a few lower bounds of the minus total domination number on a digraph $D$.
Keywords : minus total domination, digraph, tournament, lower bound
MSC numbers : 05C50, 05C69
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