The differences between global Roman domination number and Roman domination number in cubic graphs(立方图的全局罗马控制数与罗马控制数的差)

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.(图G的罗马控制函数是从G的顶点集V到集合{0,1,2}的函数f，如果图G中任意满足f(v)=0的顶点v的开邻域至少存在一个顶点u满足f(u)=2。若f是图G及其补图的罗马控制函数，则f为图G的全局罗马控制函数，∑u∈Vf(u)为（全局）罗马控制函数f的权，图G的（全局）罗马控制函数的最小权为G的（全局）罗马控制数。通过分析图的结构，根据顶点数的取值，得到了立方图的全局罗马控制数与罗马控制数的差。)