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Two graphs G and H with the same vertex set V are P₄-isomorphic if every four vertices {a,b,c,d} \subseteq V$ induce a chordless path (denoted by P₄) in G if and only if they induce a P₄ in H. We call a graph split-perfect if it is P₄-isomorphic to a ...

A clique-transversal of a graph G is a subset of vertices that meets all the cliques of G. A clique-independent set is a collection of pairwise vertex-disjoint cliques. The clique-transversal number and clique-independence number of G are the sizes of a ...

A perfect Roman dominating function on a graph G is a function f : V ( G ) ⟶ { 0 , 1 , 2 } having the property that for every vertex u with f ( u ) = 0, there exists exactly one vertex v such that u v ∈ E ( G ) and f ( v ) = 2. The ...

• We study the perfect Roman domination problem from the algorithmic point of view.