Resumen de Global signed total domination in graphs

M. Atapour, S. M. Sheikholeslami, A. Khodkar

• A function f : V (G) --> {-1, 1} defined on the vertices of a graph G is a signed total dominating function (STDF) if the sum of its function values over any open neighborhood is at least one. A STDF f of G is called a global signed total dominating function (GSTDF) if f is also a STDF of the complement G of G. The global signed total domination number ygst(G) of G is defined as ygst(G) = minf {sumatorio vEV (G) f(v) / f is a GSTDF of G}. In this paper first we find lower and upper bounds for the global signed total domination number of a graph. Then we prove that if T is a tree of order n > 4 with A(T) < n - 2, then Ygst(T) < Yst(T) + 4. We characterize all the trees which satisfy the equality. We also characterize all trees T of order n >= 4, A(T) <= n - 2 and Ygst(T) = Yst(T) + 2.