两类乘积图的符号控制数  

Signed Domination Numbers for Two Classes of Product Graphs

作　　者：徐保根 张君霞 李广 XU Baogen;ZHANG Junxia;LI Guang(Department of Mathematics,East China Jiaotong University,Nanchang 330013,China)

机构地区：[1]华东交通大学理学院

出　　处：《河南科技大学学报（自然科学版）》2020年第2期94-98,M0008,共6页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(11961026,10861032);江西省自然科学基金项目(20171BAB201009,20181BAB201002);江西省高校科技落地计划项目(KJLD12067)

摘　　要：设G=(V,E)是一个图,一个双值函数f:V→-1,+1,如果对任意顶点v∈V,均有∑u∈N[v]f(u)≥1成立,则称f为图G的一个符号控制函数。图G的符号控制数定义为γs(G)=min{∑v∈V f(v)f为图G的一个符号控制函数}。通过列举图例验证了以往研究中的部分结果是错误的,并重新确定了两类乘积图Cn×P3和Pn×P3的符号控制数。G=(V,E)is hypothesised a graph.A two-valued function f:V→{-1,+1}is said to be a signed domination function of the graph G if∑u∈N[v]f(u)≥1 holds for every vertex v∈V.The signed domination number of graph G is defined asγs(G)=min{∑v∈V f(v)f is a signed dominating function of graph G}.It is verified that the partial results of previous study is wrong by enumerating some examples of graph classes.The signed domination numbers of two classes of product graphs Cn×P3 and Pn×P3 are re-determined.

关 键 词：图 控制数 乘积图 符号控制数 

分 类 号：O157.5[理学—数学]