Roman k-domination number upon vertex and edge removal - Ghameshlou, Arezoo N.; Golmohammadi, Hamidreza; Moghaddam, S. M. Hosseini; Volkmann, Lutz (Utilitas Mathematica, 2022)
Let k ≥ 1 be an integer. A Roman k-dominatmg function on a graph G with vertex set V is a function f: V → 0,1,2 such that every vertex v ∈ V with f(v) = 0 has at least k neighbors u1,u2.-,ukwith f(ui) = 2 for i = 1,2,...,k. The weight of a Roman fc-dominating function is the value f(V) = Σu∈Vf (v). The minimum weight of Roman k-dominating functions on a graph G is called the Roman k-domination number, denoted by γkR(G). In this paper, we present bounds for the Roman k-domination number and we consider the effects of vertex and edge removal on the Roman k-domination number of a graph. © 2019 Utilitas Mathematica Publishing Inc.. All rights reserved.