Independent Double Roman Domination on Block Graphs
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Given a graph G=(V,E), f:V →{0,1,2 } is the Italian dominating function of G if f satisfies ∑_u ∈ N(v)f(u) ≥ 2 when f(v)=0. Denote w(f)=∑_v ∈ Vf(v) as the weight of f. Let V_i={v:f(v)=i},i=0,1,2, we call f the independent Italian dominating function if V_1 ∪ V_2 is an independent set. The independent Italian domination number of G is the minimum weight of independent Italian dominating function f, denoted by i_I(G). We equivalently transform the independent domination problem of the connected block graph G to the induced independent domination problem of its block-cutpoint graph T, then a linear time algorithm is given to find i_I(G) of any connected block graph G based on dynamic programming.
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