INVERSE ROMAN DOMINATION IN GRAPHS
| Autor: | L. Sudershan Reddy, M. Kamal Kumar |
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| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Discrete Mathematics, Algorithms and Applications. :1350011 |
| ISSN: | 1793-8317 1793-8309 |
| DOI: | 10.1142/s1793830913500110 |
| Popis: | 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(u) = 0 is adjacent to at least one vertex v for which f(v) = 2. For a real valued function f : V → R the weight of f is w(f) = ∑v∈V f(v). The Roman domination number (RDN) denoted by γR(G) is the minimum weight among all RDF in G. If V – D contains a roman dominating function f1 : V → {0, 1, 2}. "D" is the set of vertices v 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 [Formula: see text] is the minimum weight among all IRDF in G. In this paper we find few results of IRDN. |
| Databáze: | OpenAIRE |
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