偶图符号控制数的下界

The Lower Bounds of Signed Domination Numbers in Bipartite Graphs

设G=(V,E)是一个图,一个实值函数f:V→{-1,+1}满足∑v∈N[u]f(v)≥1对一切u∈V(G)都成立,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(G)f(v)|f为图G的符号控制函数}。研究了偶图的符号控制问题,主要给出了偶图符号控制数的两个下界。

Let G=（V, E） be a graph, a real function f：V→{-1,＋1}is said to be a signed dominating function （SDF） of Gif∑v∈N[u] f （v）≥1 holds for every vertex u∈V （G） , the signed domination number γf （G） of G is defined asγs（G）=min{∑v∈V f （v）｜f is a SDF of G}. This paper discusses some questions on the signed domination of graphs and obtains mainly two lower bounds of the signed domination numbers for bipartite graphs.