图的2-彩虹控制数的上下界  

Lower and upper bounds on the 2-rainbow domination number of a graph

作　　者：谢智红 郝国亮 庄蔚 XIE Zhihong;HAO Guoliang;ZHUANG Wei(College of Science,East China Universityof Technology,Nanchang 330013,Jiangxi,China;School of Applied Mathematics,Xiamen University of Technology,Xiamen 361024,Fujian,China)

机构地区：[1]东华理工大学理学院,江西南昌330013 [2]厦门理工学院应用数学学院,福建厦门361024

出　　处：《运筹学学报(中英文)》2024年第4期117-122,共6页Operations Research Transactions

基　　金：国家自然科学基金(Nos.12061007,11861011)。

摘　　要：图G的2-彩虹控制函数定义为从G的顶点集V(G)到集合{1,2}的幂集的函数f使得对任意满足f(v)=Ф的顶点v,均有∪_(u∈N(v))f(u)={1,2}成立,其中N(v)是顶点v的邻域。称∑_(v∈V(G))|f(v)|是图G的2-彩虹控制函数f的权。图G的2-彩虹控制数是指G的2-彩虹控制函数的最小权。通过对图的结构分析,利用图的顶点数、周长、围长以及最小度得到了图的2-彩虹控制数的一些新的上下界。A 2-rainbow dominating function of a graph G is a function f from the vertex set V(G) of G to the power set of the set {1,2} such that any vertex v with f(v)=Ф satisfies that ∪_(u∈N(v)) f(u)={1,2},where N(v) is the neighborhood of v.The value ∑_(v∈V(G))|f(v)| is called the weight of a 2-rainbow dominating function f of G.The2-rainbow domination number of G is the minimum weight of a 2-rainbow dominating function of G.By the structure analysis of graphs,some new lower and upper bounds on2-rainbow domination number of graphs are derived in terms of the number of vertices,circumference,girth and minimum degree.

关 键 词：2-彩虹控制数 周长 围长 

分 类 号：O157.5[理学—数学]