problem of deciding whether 𝜸𝒕𝑹(𝑮)=𝜸(𝑮)+𝜸𝒕𝟐(𝑮)

Roman dominating function on a graph is a function:{۰,۱,۲} satisfying the condition that every vertexfor which=۰ is adjacent to at least one vertex 𝑣 for which A total Roman dominating function is a Roman dominating function with the additional property that the subgraph of induced by the set of all vertices of positive weight has no isolated vertex. The weight of a total Roman dominating function is the value Σ. The total Roman domination number of , is the minimum weight of a total Roman dominating function in. In this paper we first study the complexity issue of the problem posed in [A. Cabrera Martinez, S. Cabrera Garcia, A. Carri_xD۸۳۵_′n Garcia,, Further results on the total Roman domination in graphs, Mathematics ۸(۳) (۲۰۲۰) ۳۴۹], and show that the problem of deciding whether is NP-complete.

کلیدواژه ها:

Total Roman dominating function ، total Roman domination number ، Semitotal Dominating set ، Dominating set ، Complexity