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Roman bondage in graphs

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Rad N., Volkmann L.

Discussiones Mathematicae Graph Theory

2011

tom 31

nr 4

763-773

A Roman dominating function on a graph G is a function f:V(G) → {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 a Roman dominating function is the value $f(V(G)) = ∑_{u ∈ V(G)}f(u)$. The Roman domination number, $γ_R(G)$, of G is the minimum weight of a Roman dominating function on G. In this paper, we define the Roman bondage $b_R(G)$ of a graph G with maximum degree at least two to be the minimum cardinality of all sets E' ⊆ E(G) for which $γ_R(G -E') > γ_R(G)$. We determine the Roman bondage number in several classes of graphs and give some sharp bounds.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Rad N.

1 Volkmann L.

1 2011

Wyniki wyszukiwania

Roman bondage in graphs