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 γ*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 nd some sharp lower and upper bounds on the k-tuple total domination number of the m-mycieleskian graph μm(g) of g in terms on k and γ*k;t(g). specially we give the sharp bounds γ*k;t(g) + 1 and γ*k;t(g) + k for γ*k;t(μ1(g)), and characterize graphs with γ*k;t(γ1(g)) = γ*k;t(g) + 1