有向图的控制数研究

项目名称： 有向图的控制数研究

项目编号： No.11301450

项目类型： 青年科学基金项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 刘娟

作者单位： 新疆师范大学

项目金额： 23万元

中文摘要： 近四十年来，随着计算机科学和网络通讯技术的飞速发展，图论研究也呈现出异常活跃的趋势，而控制数理论是其中发展最快的领域之一。图的控制数理论作为图论的一个重要研究方向，在相关学科领域，例如计算机科学、通讯网络、编码理论、运筹学以及社会学等领域具有广泛的应用。而有向图的控制理论有较强的应用背景且起步较晚，因此，还有很多问题值得去探索和挖掘。本项目选择有向图的笛卡尔积、强积、字典式积有向图，循环有向图的控制数的研究作为我们的研究基点，力争给出合理的全双控制数的概念，对一些特殊有向图类的全双控制数给出精确结果，进而对一般有向图得出较好结果。本项目的研究内容将会为工程应用提供有力的参考数据，同时丰富图的控制理论的成果，为我们进一步研究一般有向图的控制数和相关参数的上下界问题及优化问题等提供必要的研究经验和方法思路。

中文关键词： 有向图；控制数；控制集；双控制集；

英文摘要： Over the past forty years, the research on graph theory has already appeared the tendency of extremely activity with the computer science and network technology development quickly, and domination theory has become one of the fastest developing fields within graph theory. As an important research field in graph theory, domination theory has extensive application in related fields, such as computer science, communication networks, coding theory, operations search, and social sciences. Although domination theory of digraphs has the strong application background, it is still in its infancy. Thus, there are still many problems worth of exploring and mining. In the project, we choose the domintion parameters of the Cartesian product of digraphs、strong product of digraphs、lexicographic product of digraphs and circulant digraph as the main starting point of our research. striving to propose reasonable concept for total twin domination number, the accurate results are given for some specail class of digraphs, then more and better research results for general digraph about their domination number will be given. The research contents and results of the project will provide cogent reference data for application in Engineering, enrich the results of the domimation theory of graphs, and provide the necessary research experie

英文关键词： digraph；domination number；dominating set；twin dominating set；