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 u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. The weight of a Roman dominating function f is the value f(V(G)) = Σu∊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 continue the study of Roman domination edge critical graphs by giving several properties and characterizations for these graphs.
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