关于图的符号星控制数

On Signed Star Domination Numbers of Graphs

设G=(V,E)是一个图,u∈V,则E(u)表示u点所关联的边集.一个函数f:E→{-1,1}如果满足■f(e)≥1对任意v∈V成立,则称f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{■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.