图的控制数的Hopfield网络模型和算法

The Neural Network Model and Algorithm of Domination Number of Graphs

对图G(V ,E) ,及二值函数 f:V→ { 0 ,1}记 f[v]={u｜u∈N[v],且f(u) =1} ,其中N[v]={u｜vu∈E} ∪ {v} .若 f满足任意v∈V ,｜f[v]｜≥ 1,则称f为G的一控制函数 ,并称 f(V) = v∈Vf(v)为 f的权 ;图的控制数γ(G)定义为图的控制函数的最小权 ,即γ(G) =min{ ｜f(V) ｜f为G的一控制函数 } .类似的可定义图的边控制数 .本文建立了确定图的控制数的Hopfield网络型和算法 .

Let G(V,E) be a graph,a two-value functionf:V→｛0,1｝ is a domination function of G if its function value over any closed neighborhood is at least one.The weight of a domination function is f(V)=v∈Vf(v).The domination number of a graph G,denoted by γ(G), equals the minimum weight of a domination function of G.In this paper, a neural network model of the domination number problem is constructed and the algorithm is studied.