有关图的弱罗马控制数的一些结论

Some Results of Weak Roman Domination Number in Graphs

图的弱罗马控制数是图的弱罗马控制函数(简称WRDF)的最小权,记为γr(G).本文确定了完全n部图的弱罗马控制数,根据罗马控制数的下界以及弱罗马控制数与罗马控制数、控制数之间的关系,确定了弱罗马控制数的下界,运用概率方法给出了弱罗马控制数的上界.

The weak Roman domination number of graphs,denoted by γ_r(G),is the minimum weight of a weak Roman dominating function(WRDF) in graphs.In this paper,we determine the weak Roman domination number of the complete n-partite graph.Based on the lower bound of Roman domination number and the connection among the weak Roman domination number,the Roman domination number and the domination number,we determine the lower bound of weak Roman domination number.Using a probabilistic method,an upper bound of weak Roman domination number is obtained.