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Roman domination in regular graphs
A Roman domination function on a graph G=(V(G),E(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 ...
Roman domination on strongly chordal graphs
Given real numbers b a >0, an ( a , b )- Roman dominating function of a graph G =( V , E ) is a function f : V {0, a , b } such that every vertex v with f ( v )=0 has a neighbor u with f ( u )= b . An independent/connected/total ...
Perfect Roman domination in graphs
AbstractA 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 ...
Highlights- We study the perfect Roman domination problem from the algorithmic point of view.
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