Upper bounds on the upper signed total domination number of graphs Original Research Article

Let image be a graph. A function image defined on the vertices of image is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. A signed total dominating function image is minimal if there does not exist a signed total dominating function image, image, for which image for every image. The weight of a signed total dominating function is the sum of its function values over all vertices of image. The upper signed total domination number of image is the maximum weight of a minimal signed total dominating function on image. In this paper we present a sharp upper bound on the upper signed total domination number of an arbitrary graph. This result generalizes previous results for regular graphs and nearly regular graphs.