International Journal of Trend in Scientific Research and Development

Let G = V, E be a simple graph. A subset D of V G is called a total strong dominating set of G, if for every u V G , there exists a v D such that u and v are adjacent and deg v = deg u . The minimum cardinality of a total strong dominating set of G is called total strong domination number of G and is denoted by s t G . Corresponding to total strong dominating set of G, total strong dominating function can be defined. The minimum weight of a total strong dominating function is called the fractional total strong domination number of G and is denoted by t sf G . A study of total strong dominating functions is carried out in this paper