中文摘要：

利用图论的方法研究了图G同其补图G的Roman控制数，得到了完全图和完全多部图的补图的Roman控制数及图G同其补图G的Roman控制数的关系；还研究了图G的生成子图H同G的Roman控制数的关系和极大无完美匹配的简单图G的Roman控制数.

英文摘要：

The relation between the Roman domination numbers of graph G and its complement graph was studied. The Roman domination number of the complement of the complete graph and multicomplete graph was obtained. It is found tha the relation of Roman domination number between the graph G and its complete graph G. The relation between Roman domination number of graph G and its spanning sub-graph H was proposed and the domination number of the graph G in which there is no maximal oerfect matching was discussed.