Global minus domination in graphs

Document Type: Research Paper

Authors

1 University of Bonab

2 Azarbaijan Shahid Madani University

Abstract

‎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.

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