On the Mixed Minus Domination in Graphs

作     者：Baogen Xu Xiangyang Kong 

作者机构：Department of MathematicsEast China Jiaotong UniversityNanchangJiangxi 330013China 

出 版 物：《Journal of the Operations Research Society of China》 (中国运筹学会会刊（英文）)

年 卷 期：2013年第1卷第3期

页      面：385-391页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work was supported by the National Natural Science Foundation of China(No.11061014,11361024,11261019) the Science Foundation of Jiangxi Province(No.KJLD12067) The authors are grateful to the referees for their careful reading with corrections and especially the referee who draws our attention to the proof in Theorem 2.2,which let us improve the proof of Theorem 2.2,and correct this lower bound 

主　　题：Mixed minus domination function Mixed minus domination number 

摘      要：Let G=(V,E)be a graph,for an element x∈V∪E,the open total neighborhood of x is denoted by N_(t)(x)={y|y is adjacent to x or y is incident with x,y∈V∪E},and Nt[x]=Nt(x)∪{x}is the closed one.A function f:V(G)∪E(G)→{−1,0,1}is said to be a mixed minus domination function(TMDF)of G if∑_(y∈Nt[x])f(y)≥1 holds for all x∈V(G)∪E(G).The mixed minus domination numberγ′_(tm)(G)of G is defined as γ′_(tm)(G)=min{∑x∈V∪E f(x)|f is a TMDF of G.In this paper,we obtain some lower bounds of the mixed minus domination number of G and give the exact values ofγ′_(tm)(G)when G is a cycle or a path.