Abstract
A Roman dominating function of a graph G is a labeling f: V(G) → {0, 1, 2} such that every vertex with label 0 has a neighbor with label 2. The Roman domination number γR(G) of G is the minimum of Σv∊V(G) f(v) over such functions. The Roman domination subdivision number sdγR (G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the Roman domination number. In this paper, we establish upper bounds for the Roman domination subdivision number of graphs.
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