Signed Total Domination and Mycielski Structure in Graphs

Let G = (V, E) be a graph. The function f : V (G) -> {-1, 1} is a signed total dominating function if for every vertex v is an element of V (G), Sigma(x is an element of NG(v)) f(x) >= 1. The value of omega(f) = Sigma(x is an element of V (G)) f(x) is called the weight of f. The signed total domination number of G is the minimum weight of a signed total dominating function of G. In this paper, we initiate the study of the signed total domination numbers of Mycielski graphs and find some upper bounds for this parameter. We also calculate the exact value of the signed total domination number of the Mycielski graph when the underlying graph is a special graph.