Universal minimal total dominating functions in graphs

A total dominating function (TDF) of a graph G = ( V, E ) is a function f : V → [0, 1] such that for each ν ϵ V , Σ uϵN(v) f(u) ⩾ 1 [where N(v) denotes the open neighborhood of vertex v ]. Integer‐valued TDFs are precisely characteristic functions of total dominating sets of G . Convex combinations of two TDFs are themselves TDFs but convex combinations of minimal TDFs (MTDFs) are not necessarily minimal. This paper is concerned with the existence of a universal MTDF in a graph, i.e., a MTDF g such that convex combinations of g and any other MTDF are themselves minimal. © 1994 by John Wiley & Sons, Inc.