Changing and unchanging the Roman domination number of a graph

Abstract

A Roman dominating function on a graph G with vertex set V(G) is a function f : V(G) ↠ {0, 1, 2} satisfying the condition that every vertex it with f(u) = 0 is adjacent to at least one vertex v with f(v) = 2. The weight of a Roman dominating function is the value f(V(G)) = Σ_u⋯V(G) f(u). The Roman domination number _γR(G) of G is the minimum weight of a Roman dominating function on G. In this paper, we study how the Roman domination number changes by means of removing a vertex or an edge from a graph.