Communications of the
Korean Mathematical Society CKMS

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