弱罗马控制数与最小控制数相同的树

Trees T with Weak Roman Domination Number Being Equal to Domination Number

Henning M A等提出了图的弱罗马控制数(记为γ_r(G))的概念,给出了弱罗马控制数与最小控制数相同的图(即γ(G)=γ_r(G))的特征.树是无圈的连通图,相同条件下它除了满足上述的特征外,还具有自身的特点.运用递归法和指标函数法,刻画了弱罗马控制数与最小控制数相同的树(即γ(T)=γ_r(T))的特征.

M.A.Henning defined the weak Roman domination number（denoted γ_r（G）） on a graph,and characterized graphs for which γ_r（G） = γ（G）.Because the tree is the connection graph with no cycle,in the same condition,it doesn＇t only satisfy the upper character,but also possess itself character.In this paper,by the devices of recursion and index function,we characterize trees T for which γ_r（T） = γ（T）.