Critical graphs with Roman domination number four

Abstract

A Roman domination function on a graph G is a function satisfying the condition that every vertex u for which r(u) = 0 is adjacent to at least one vertex v for which r(v) = 2. The weight of a Roman domination function is the value The Roman domination number of G is the minimum weight of a Roman domination function on G. “Roman Criticality” often refers to the study of graphs where the Roman domination number decreases when adding an edge or removing a vertex of the graph. In this paper we add some condition to this notion of criticality and give a complete characterization of critical graphs with Roman Domination number

Keywords

• roman domination
• critical