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)) = åu Î V(G) f (u){f (V(G)) = sum_{uin V(G)} f (u)}. The Roman domination number, γ R (G), of G is the minimum weight of a Roman dominating function on G. The Roman bondage number b R (G) of a graph G with maximum degree at least two is the minimum cardinality of all sets E¢ Í E(G){E^{prime} subseteq E(G)} for which γ R (G − E′) > γ R (G). In this paper we present different bounds on the Roman bondage number of planar graphs.
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机译：图G上的罗马支配函数是函数f：V（G）→{0，1，2}满足以下条件：每个顶点f（u）= 0都与至少一个顶点v相邻。 f（v）=2。一个罗马支配函数的权重是值f（V（G））=å uÎV（G） f（u）{f（V（G） ）= sum_ {uin V（G）} f（u）}。 G的罗马支配数γ R （G）是G上罗马支配函数的最小权重。a的罗马束缚数b R （G）最大度至少为2的图G是所有集γ R （G-E'）>γ R （G）。在本文中，我们提出了平面图的罗马束缚数的不同界限。
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