Global minus domination in graphs

‎A function f:V(G)\rightarrow \{-۱,۰,۱\} is a minus‎ ‎dominating function if for every vertex v\in V(G)‎, ‎\sum_{u\in‎ ‎N[v]}f(u)\ge ۱‎. ‎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.

Keywords:

minus dominating function , minus domination number , global minus dominating function , global minus domination number