Upper bounds on the upper signed total domination number of graphs

Abstract: Let be a graph. A function defined on the vertices of 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 is minimal if there does not exist a signed total dominating function , , for which for every . The weight of a signed total dominating function is the sum of its function values over all vertices of . The upper signed total domination number of is the maximum weight of a minimal signed total dominating function on . 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. [Copyright &y& Elsevier]