Minus total domination in graphs
Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 861-870
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A three-valued function $f\: V\rightarrow \{-1,0,1\}$ defined on the vertices of a graph $G=(V,E)$ is a minus total dominating function (MTDF) if the sum of its function values over any open neighborhood is at least one. That is, for every $v\in V$, $f(N(v))\ge 1$, where $N(v)$ consists of every vertex adjacent to $v$. The weight of an MTDF is $f(V)=\sum f(v)$, over all vertices $v\in V$. The minus total domination number of a graph $G$, denoted $\gamma _t^{-}(G)$, equals the minimum weight of an MTDF of $G$. In this paper, we discuss some properties of minus total domination on a graph $G$ and obtain a few lower bounds for $\gamma _t^{-}(G)$.
@article{CMJ_2009__59_4_a0,
author = {Xing, Hua-Ming and Liu, Hai-Long},
title = {Minus total domination in graphs},
journal = {Czechoslovak Mathematical Journal},
pages = {861--870},
publisher = {mathdoc},
volume = {59},
number = {4},
year = {2009},
mrnumber = {2563563},
zbl = {1224.05387},
language = {en},
url = {http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a0/}
}
Xing, Hua-Ming; Liu, Hai-Long. Minus total domination in graphs. Czechoslovak Mathematical Journal, Tome 59 (2009) no. 4, pp. 861-870. http://geodesic.mathdoc.fr/item/CMJ_2009__59_4_a0/