广义Sierpiński网络的全控制数

Total domination number of generalized Sierpiński networks

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}.该文应用数学归纳法和分类讨论法,得到了以路P_(m)、圈C_(m)、完全图K_(m)为基图的广义Sierpiński网络的全控制数.

A total dominating 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 dominating function on G is the sum f(V)=∑v∈V f(v)and the total dominating numberγt(G)is the minimum weight of an total dominating function.In this paper,the methods of mathematical induction and classification discussion are mainly used to obtain the total domination number of the generalised Sierpiński networks based on Path P m,Cycle C_(m)and Complete graph K_(m).