Roman bondage numbers of some graphs

A Roman dominating function on a graph G = (V,E) is a function f : V → {0, 1, 2} satisfying the condition that every vertex u with f(u) = 0 is adjacent to at least one vertex v with f(v) = 2. The weight of a Roman dominating function is the value f(G) = ∑ u∈V f(u). The Roman domination number of G is the minimum weight of a Roman dominating function on G. The Roman bondage number of a nonempty graph G is the minimum number of edges whose removal results in a graph with the Roman domination number larger than that of G. This paper determines the exact value of the Roman bondage numbers of two classes of graphs, complete t-partite graphs and (n − 3)-regular graphs with order n for any n ≥ 5.