基于完全二部图K_(m,n)的广义Sierpiński网络的全控制数

Total Domination Number of Generalized Sierpiński Networks Based on Complete Bipartite Graph K_(m,n)

设G=(V,E)为一个无孤立点的图,如果一个双值函数f:V→{0,1}对任意点v∈V,均有f(N(v))≥1成立,则称f为图G的一个全控制函数.图G的全控制数定义为γt(G)=min{f (V)|f为图G的一个全控制函数}.主要应用数学归纳法和分类讨论思想,得到了以完全二部图K_(m,n)为基图的广义Sierpinski网络的全控制数.

A total domination function of a graph G=(V,E) is a function f:V→{0,1}satisfying the condition that for every v∈V with f(N(v))≥ 1.The weight of a total domination function on G is the sum f(V)=∑v∈Vf(v) and the total domination number,γt(G) is the minimum weight of a total domination function.In this paper,the methods of mathematical induction and classification discussion are mainly used to obtain the total domination number of the generalized Sierpinski networks based on complete bipartite graph.