Total dominating functions in trees: Minimality and convexity
E. J. Cockayne, Christina M. Mynhardt, Bo Yang Yu · Journal of Graph Theory · 1995
Abstract 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 neighbors of vertex v). Convex combinations of TDFs are also TDFs. However, convex combinations of minimal TDFs (i.e., MTDFs) are not necessarily minimal. In this paper we discuss the existence in trees of a universal MTDF (i.e., an MTDF whose convex combinations with any other MTDF are also minimal). © 1995 John Wiley & Sons, Inc.