Global Signed Domination in Graphs

A function f : V(G)→{−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) →{−1,1} is called a global signed dominating function (GSDF) if f is also a SDF of the complement G of G. The global signed domination number γgs(G) of G is defined as γgs(G) = min{Σv∈V(G) f (v) | f is a GSDF of G}. In this paper we study this parameter and pose some open problems.