k-TUPLE TOTAL DOMINATION AND MYCIELESKIAN GRAPHS
نویسندگان
چکیده
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 find 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(μ1(G)) = γ×k,t(G) + 1.
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