有向de Bruijn图与广义有向de Bruijn图的罗马控制数  

The Roman Domination Numbers of the Directed de Bruijn and Generalized Directed de Bruijn Graphs

作　　者：张新鸿[1] 郭亚丽 ZHANG Xinhong;GUO Yali(School of Applied Science,Taiyuan University of Science and Technology,Taiyuan 030024,China)

机构地区：[1]太原科技大学应用科学学院,山西太原030024

出　　处：《山西大学学报（自然科学版）》2023年第5期1042-1049,共8页Journal of Shanxi University(Natural Science Edition)

基　　金：山西省基础研究计划(20210302123202)。

摘　　要：文章研究了有向de Bruijn图与广义有向de Bruijn图的控制结构,通过构造同态映射给出了有向de Bruijn图的控制数,进而利用数学归纳法完整地刻画了有向de Bruijn图的罗马控制数。在此基础上,运用分类分析法进一步给出了广义有向de Bruijn图的罗马控制数的紧界。In this paper,the dominating structures of the directed de Bruijn and generalized directed de Bruijn graphs are studied,and the domination number of the directed de Bruijn graphs is given by constructing a homomorphic map.Then we completely charac-terize the Roman domination number of a directed de Bruijn graph using mathematical induction.On this basis,the sharp bound of the Roman domination number of the generalized directed de Bruijn graph is further given by using the classification analysis method.

关 键 词：同态映射 控制集 控制函数 正则 

分 类 号：O157.5[理学—数学]