Global minus domination in graphs
نویسندگان
1 Azarbaijan Shahid Madani University
2 Azarbaijan Shahid Madani University
3 University of Bonab
doi
10.22108/toc.2014.4989چکیده
A function $f:V(G)\rightarrow \{-1,0,1\}$ is a minus dominating function if for every vertex $v\in V(G)$, $\sum_{u\in N[v]}f(u)\ge 1$. A minus dominating function $f$ of $G$ is called a global minus dominating function if $f$ is also a minus dominating function of the complement $\overline{G}$ of $G$. The global minus domination number $\gamma_{g}^-(G)$ of $G$ is defined as $\gamma_{g}^-(G)=\min\{\sum_{v\in V(G)} f(v)\mid f \;{\rm is\; a\; global\; minus\; dominating\; function}\\ {\rm of }\; G\}$. In this paper we initiate the study of the global minus domination number in graphs and we establish lower and upper bounds for the global minus domination number.
