Roman k-domination number upon vertex and edge removal

Abstract

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.-,u_kwith f(u_i) = 2 for i = 1,2,...,k. The weight of a Roman fc-dominating function is the value f(V) = Σ_u∈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.