一些特定图类的严格强控制数

Strict Majority Domination Number of Some Certain Families of Graphs

设图G=(V,E),对于函数f:V→ ｛- 1,1 ｝,记f的权重f(V) =∑v∈Vf(v),对v∈V,记f[v]=∑u∈N[v]f(u).图G的严格强控制函数是f:V→｛- 1,1 ｝使得对V中多于一半的顶点v有f[v]≥1,图G的严格强控制数是G的所有严格强控制函数的量小权重,且用smaj(G)表示.

Let G=(V,E) be a graph.For a function f:V→{-1,1}, the weight of f is f(V)=∑v∈Vf(v) .For a vertex v in V ,we define f=∑u∈Nf(u) .A strict majority dominating function of G is a function f:V→{-1,1} ,such that f≥1 for more than half of the vertices in V .The strict majority dmination number is the minimum possible weight of all strict mojority dominating function,and is denoted as smaj (G) .We determine the strict majority domination numbers of some certain families of graphs.