两类联图的符号控制数  

Signed Domination Number of Two Classes Join Graph

作　　者：张靖宇 红霞[1] ZHANG Jingyu;HONG Xia(Department of Mathematics,Luoyang Normal University,Luoyang 471022,Henan,China)

机构地区：[1]洛阳师范学院数学科学学院,河南洛阳471022

出　　处：《汕头大学学报（自然科学版）》2020年第3期21-31,共11页Journal of Shantou University：Natural Science Edition

基　　金：国家自然科学基金资助项目(11701257);河南省教育厅高校重点项目资助项目(18A110025)(2018XJGGJS-10)。

摘　　要：设图G=(V,E)为一个图,一个双值函数f:V→{1,-1},若S?V,则记f(S)=Σv∈s f(v).如果对任意的顶点v∈V,均有f(N[v])≥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{f(V) f是图G的一个符号控制函数}.联图G=■∨H是空图■的每个顶点都与图H的每个顶点相连接而成的图.本文主要利用讨论图中-1顶点个数的方法得到下界和用标号法得到上界,从而确定两类联图的符号控制数的精确值,即确定了γS(■∨Kn)和γS(■∨W1·n).Let G=(V,E)be a graph and denotes f(S)=∑v∈Sf(v)for S?V. A function f : V→{1,-1} is said to be a signed domination function(SDF), if f(N[v])≥1 for v∈V. The signed domination number is γS(G)=min{ f(V) f is an SDF of G}. The join graph G=■∨H is a graph obtained by every vertex of empty graph ■ adjacent to each vertex of graph H. In this paper, the lower bound is obtained by using the method of discussing the number of-1 vertices in the graph, and the upper bound is obtained by labeling method,and therefore we determine exact values of the signed domination number of two classes join graph, which are γS(■∨Kn)and γS(■∨W1·n).

关 键 词：符号控制函数 符号控制数 联图 

分 类 号：O157.5[理学—数学]