Roman Domination
نویسنده
چکیده
In his article published in 1999, Ian Stewart discussed a strategy of Emperor Constantine for defending the Roman Empire. Motivated by this article, Cockayne et al.(2004) introduced the notion of Roman domination in graphs. Let G = (V,E) be a graph. A Roman dominating function of G is a function f : V → {0, 1, 2} such that every vertex v for which f(v) = 0 has a neighbor u with f(u) = 2. The weight of a Roman dominating function f is w(f) = ∑ v∈V f(v). The Roman domination number of a graph G, denoted by γR(G), is the minimum weight of all possible Roman dominating functions. This expository paper examines the bounds of Roman domination number and provides examples of calculating this quantity in special graphs such as path, cycles, circulant graphs and regular graphs. In addition, we show the bound for Roman domination number for a connected graph of order n is bounded by b4n/5c in general. Lastly we look at a local property of Roman domination number, namely the effect of adding an edge to a graph.
منابع مشابه
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