k-TUPLE TOTAL DOMINATION AND MYCIELESKIAN GRAPHS

Let k be a positive integer. A subset S of V(G) in a graph G is a k-tuple total dominating set of G if every vertex of G has at least k neighbors in S. The k-tuple total domination number gamma x k,t (G) of G is the minimum cardinality of a k-tuple total dominating set of G. In this paper for a given graph G with minimum degree at least k, we find some sharp lower and upper bounds on the k-tuple total domination number of the m-Mycieleskian graph mu(m) (G) of G in terms on k and 7x k (G). Specially we give the sharp bounds gamma x k,t(G) + 1 and gamma x k,t (G) k for gamma x k,t (mu(1)(G)), and characterize graphs with gamma xk,t (mu(1)(G)) = gamma x k,t (G) + 1.