A characterisation of universal minimal total dominating functions in trees Original Research Article

A total dominating function (TDF) of a graph G=(V, E) is a function f : V → [0, 1] such that for each v ϵ V, ΣuϵN(v)f(u)⩾ 1, where N(v) denotes the set of neighbours of v. Although convex combinations of TDFs are also TDFs, convex combinations of minimal TDFs (MTDFs) are not necessarily minimal. An MTDF whose convex combinations with any other MTDF are minimal is called a universal MTDF. In this paper we characterise universal MTDFs for trees.