The differences between global Roman domination number and Roman domination number in cubic graphs
A Roman dominating function of a graph G is a function f from the vertex set V of G to the set {0,1,2} if the open neighbor of any vertex v of G with f(v)=0 has at least one vertex u with f(u)=2.If a function f is a Roman dominating function of a graph G and its complement,then f is called a global Roman dominating function of G.The∑u∈Vf(u)is called the weight of a(global)Roman dominating function f of G.The(global)Roman domination number of G is the minimum weight of a(global)Roman dominating function of G.By analyzing the structure of graphs,according to the number of vertices of cubic graphs,the differences between global Roman domination number and Roman domination number are obtained.
global Roman dominationRoman dominationcubic graphcomplement
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