INVERSE ROMAN DOMINATION IN GRAPHS

Motivated by the article in Scientific American [7], Michael A Henning and Stephen T Hedetniemi explored the strategy of defending the Roman Empire. Cockayne defined Roman dominating function (RDF) on a Graph G = (V, E) to be a function f : V -> {0, 1, 2} satisfying the condition that every vertex u for which f(upsilon) = 0 is adjacent to at least one vertex upsilon for which f(upsilon) = 2. For a real valued function f : V -> R the weight of f is w(f) = Sigma(upsilon is an element of V) f(v). The Roman domination number (RDN) denoted by (gamma R)(G) is the minimum weight among all RDF in G. If V - D contains a roman dominating function f(1) : V. {0, 1, 2}. "D" is the set of vertices upsilon for which f(v) > 0. Then f1 is called Inverse Roman Dominating function (IRDF) on a graph G w.r.t. f. The inverse roman domination number (IRDN) denoted by gamma(1)(R) (G) is the minimum weight among all IRDF in G. In this paper we find few results of IRDN.