全局3-彩虹控制数等于顶点数的图的刻画  

A Characterization of Graphs with Global 3-Rainbow Domination Number Equal to the Number of Vertices

作　　者：郝国亮 曾淑婷 HAO GUOLIANG;ZENG SHUTING(School of Mathematics and Statistics,Heze University,Heze 274015,China;College of Science,East China University of Technology,Nanchang 330013,China;Ruijin No.1 High School,Ganzhou 342506,China)

机构地区：[1]菏泽学院数学与统计学院,菏泽274015 [2]东华理工大学理学院,南昌330013 [3]瑞金第一中学,赣州342506

出　　处：《应用数学学报》2024年第3期417-428,共12页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(批准号:12061007);菏泽学院博士基金项目(批准号:XY23BS12,XY23BS48);江西省研究生创新专项资金项目(YC2021-S628)资助。

摘　　要：图G的3-彩虹控制函数是指从G的顶点集V到集合{1,2,3}的幂集的映射f,使得任意满足f(v)=■的顶点v均有∪u∈N(ν)={1,2,3}成立,其中N(v)是顶点v的邻域.图G的3-彩虹控制函数f的权为∑ν∈V|f(ν)|.如果f既是图G又是其补图的3-彩虹控制函数,则称f为图G的全局3-彩虹控制函数.图G的全局3-彩虹控制数是指G的全局3-彩虹控制函数的最小权.通过对图的结构分析,利用分类讨论法完全刻画了全局3-彩虹控制数等于顶点数的所有图.A 3-rainbow dominating function of a graph G is a mapping f from the vertex set V of G to the power set of the set(1,2,3)such that any vertex with f(u)=satisfies that∪u∈N(ν)={1,2,3},where N(u)is the neighborhood of v.The weight of a 3-rainbow dominating function f of G is∑ν∈V|f(ν)|.If f is a 3-rainbow dominating function of a graph G and its complement,then f is called a global 3-rainbow dominating function of G.The global 3-rainbow domination number of G is the minimum weight of a global 3-rainbow dominating function of G.By analyzing the structure of graphs,using the method of categorical discussion,we completely characterize the graphs with global 3-rainbow domination number equal to the number of vertices.

关 键 词：全局3-彩虹控制函数 全局3-彩虹控制数 补图 

分 类 号：O157.5[理学—数学]