一类联图的符号控制数  

The Signed Domination Number of a Join Graph

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

机构地区：[1]洛阳师范学院数学科学学院

出　　处：《宜春学院学报》2019年第6期3-9,共7页Journal of Yichun University

基　　金：国家自然科学基金(No.11701257,No.11801253,No.11571005);河南省教育厅高校重点项目(No.18A110025,No.18A110026);河南省科技计划项目(182102310930,182102310955,2017-JSJYYB-074,2017xjjg054)

摘　　要：设图G=(V,E)为一个图,一个双值函数f:V→{1,-1},若SV,则记f(S)=∑v∈Sf(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}图G=Km∨Pn表示图Km的每个顶点与路Pn的每个顶点相连接的联图。本文主要用分类讨论法和穷标法得到了图G的符号控制数的精确值,即确定了γs(Km∨Pn)。特别地,此联图中当m=1时得到了扇图的符号控制数,从而推广了已知结果。Let G =( V,E) be a graph and denotes f(S)=∑ v∈S f(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 γ s(G)= min {f(V)|f is an SDF of G . G= K m ∨P n denote is a graph obtained by every vertex of K m is adjacent to each vertex of path P n . In this paper, we determine exact values of the signed domination number of a join graph by exhaustive method and classified discussion, which is γ s( K m ∨P n). Specially, we give the signed domination number of Fan graph for m=1 , which generalize the known result.

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]