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On The Roman Domination Stable Graphs

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Hajian M., Rad N. J.

Discussiones Mathematicae Graph Theory

2017

tom 37

nr 4

859-871

A Roman dominating function (or just RDF) on a graph G = (V,E) is 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. The weight of an RDF f is the value f(V (G)) = Pu2V (G) f(u). The Roman domination number of a graph G, denoted by R(G), is the minimum weight of a Roman dominating function on G. A graph G is Roman domination stable if the Roman domination number of G remains unchanged under removal of any vertex. In this paper we present upper bounds for the Roman domination number in the class of Roman domination stable graphs, improving bounds posed in [V. Samodivkin, Roman domination in graphs: the class RUV R, Discrete Math. Algorithms Appl. 8 (2016) 1650049].

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Hajian M.

1 Rad N. J.

1 2017

Wyniki wyszukiwania

On The Roman Domination Stable Graphs