Volume 36 • Number 2 • 2013   • Global Signed Domination in Graphs H. Karami, R. Khoeilar, S. M. Sheikholeslami and Abdollah Khodkar Abstract. A function $f:V(G)\rightarrow \{-1,1\}$ defined on the vertices of a graph $G$ is a signed dominating function (SDF) if the sum of its function values over any closed neighborhood is at least one. A SDF $f:V(G)\rightarrow \{-1,1\}$ is called a global signed dominating function (GSDF) if $f$ is also a SDF of the complement $\overline{G}$ of $G$. The global signed domination number $\gamma_{gs}(G)$ of $G$ is defined as $\gamma_{gs}(G)=\min\{\sum_{v\in V(G)} f(v)\mid f \mbox{ is a GSDF of } G\}$. In this paper we study this parameter and pose some open problems. 2010 Mathematics Subject Classification: 05C69, 05C05 Full text: PDF