For a connected graph G = (V, E) of order at least two, subset T minimum total monophonic set S is forcing for if the unique containing . A cardinality S. The number ftm(S) in ftm(G) min{ftm(S)}, where taken over all sets G. We determine bounds it and find certain classes graphs. It shown that every pair a, b positive integers with 0 ≤ < ≥ a+4, there exists such mt(G) b.