on total domination number of middle of known graphs

A total dominating set of a graph g with no isolated vertices is a subset s of thevertex set such that every vertex of g is adjacent to a vertex in s. the total dominationnumber of g is the minimum cardinality of a total dominating set of g. in this paper, westudy the total domination number of middle graphs. indeed, we obtain tight bounds for thisnumber in terms of the order of the graph g. we also compute the total domination number ofthe middle graph of some known families of graphs explicitly.