设G=(VE)是一个图,V∈V,则E(v)表示v点所关联的边集.一个函数,f:E→{-1,1)如果满足∑ e∈E(v)f(e)≥1对任意v∈V成立,则称.厂为图G的一个符号星控制函数,图G的符号星控制数定义为γ'ss(G)=min{∑ e∈E f(e):f为图G的一个符号星控制函数}.给出了几类特殊图的符号星控制数,主要包含完全图,正则偶图和完全二部图.
Let G= (V, E) be a graph, v ∈ VthenE(v)denotes the set of edges adjacent to v. A function f : E → (-1, 1)is said to be a signed star dominating function (SSDF) of G if ∑ e∈E(v)f(e)≥1 holds for every vertex v ∈ V, the signed star domination number of Gis defined as γ'ss(G)=min{∑ e∈E f(e):f is an SSDF of G}. In this paper we give the signed star domination numbers for several classes of graphs, these contain the complete graphs, regular even graphs and complete bipartite graphs.