Publications Repository - Gdańsk University of Technology

A Roman dominating function on a graph G=(V,E) is defined to be a function f :V → {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. A dominating set D⊆V is a weakly connected dominating set of G if the graph (V,E∩(D×V)) is connected. We define a weakly connected Roman dominating function on a graph G to be a Roman dominating function such that the set {u ∈ V : f(u) ∈{1,2}} is a weakly connected dominating set of G. The weight of a weakly connected Roman dominating function is the value f(V) =∑u∈V f(u). The minimum weight of a weakly connected Roman dominating function on a graph G is called the weakly connected Roman domination number of G and is denoted by γ wc R (G). In this paper, we initiate the study of this parameter.

Authors

• dr inż. Joanna Raczek link open in new tab ,
• dr Joanna Cyman link open in new tab