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 is minimal if there does not exist a STDF
g:V(G)→{−1,1},
f≠g, for which
g(v)≤f(v) for every
vV(G). The weight of a STDF is the sum of its function values over all vertices. The signed
total domination number of
G is the minimum weight of a STDF of
G, while the upper signed
total domination number of
G is the maximum weight of a minimal STDF on
G. In this paper we study these two parameters. In particular, we present lower bounds on the signed
total domination number and upper bounds on the upper signed
total domination number of a graph.