k-TUPLE TOTAL DOMINATION AND MYCIELESKIAN GRAPHS

Abstract. 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 ?_(×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 ?_(m)(G) of G in terms on k and ?_(×k,t) (G). Specially we give the sharp bounds ?_(×k,t) (G)+1 and ?_(×k,t) (G)+k for ?_(×k,t) (?_1 (G)), and characterize graphs with ?_(×k,t) (?_1 (G))=?_(×k,t)(G)+1.