立方图的全局罗马控制数与罗马控制数的差  

The differences between global Roman domination number and Roman domination number in cubic graphs

作　　者：谢智红 吴愉琪 郝国亮 姜海宁 XIE Zhihong;WU Yuqi;HAO Guoliang;JIANG Haining(School of Business,Heze University,Heze 274015,Shandong Province,China;College of Science,East China University of Technology,Nanchang 330013,China;School of Mathematics and Statistics,Heze University,Heze 274015,Shandong Province,China)

机构地区：[1]菏泽学院商学院,山东菏泽274015 [2]东华理工大学理学院,江西南昌330013 [3]菏泽学院数学与统计学院,山东菏泽274015

出　　处：《浙江大学学报（理学版）》2024年第5期572-579,共8页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(12061007);菏泽学院博士基金项目(XY23BS12,XY23BS48).

摘　　要：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,Σ_(u∈V)f(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。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 Σ_(u∈V)f(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.

关 键 词：全局罗马控制 罗马控制 立方图 补图 

分 类 号：O157.5[理学—数学]