Peakless functions on graphs Original Research Article

Let G = (V, E) be a finite connected graph, endowed with the standard graph-metric d(u, v). A real valued function f defined on V is called peakless if d(u, w) + d(w, v) = d(u, v) implies f(w) ⩽ max{f(u), f(v)} and equality holds only if f(u) = f(v) (see Busemann, (1955) for the general definition). Peakless functions inherit and generalize the properties of usual convex functions.