Total {K}-Domination In Special Graphs

For a positive integer k and a graph G = (V, E), a function f : V -> {0, 1, ..., k} is called a total {k}-dominating function of G if Sigma(u is an element of NG)(v) f(u) >= k for each v is an element of V, where N-G (v) is the neighborhood of v in G. The total {k}domination number of G, denoted by gamma({k})(t) (G), is the minimum weight of a total {k}-dominating function G, where the weight of f is Sigma(v is an element of V) f(v). In this paper, we determine the exact values of the total {k}-domination number for several commonly-encountered classes of graphs including cycles, paths, wheels, and pans.