Critical properties on Roman domination graphs
نویسندگان
چکیده
A Roman domination function on a graph G is a function r : V (G) → {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman function is the value r(V (G)) = ∑ u∈V (G) r(u). The Roman domination number γR(G) of G is the minimum weight of a Roman domination function on G . "Roman Criticality" has been defined in general as the study of graphs were the Roman domination number decreases when removing an edge or a vertex of the graph. In this paper we give further results in this topic as well as the complete characterization of critical graphs that have Roman Domination number γR(G) = 4.
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