【作者】 胡红萍；

【导师】 王建中；

【作者基本信息】 华北工学院 ， 系统工程， 2002， 硕士

【摘要】 本文主要进行有向图Hamilton性质的研究。在JorgenBang—Jense「7」提出了有向图为有向Hamilton图的两个新充分条件及徐尚进副教授「11」提出有向图为哈密顿图的—个充要条件等前人所研究的主要结果的基础上，根据大量的图形特征以及有向图的邻接矩阵的特性，提出有向图以及严格有向二部图具有有向Hamilton路或者为有向Hamilton图的度充分条件，还提出利用有向图的邻接矩阵去研究有向图的Hamilton性质，进而利用图论的相关知识点以及代数学等给出相应地论证过程。第1章，主要论述了有向图及有向图的Hamilton性质的相关结果，并对本论文的研究过程及相关结果做了系统地论述。第2章，主要论述了在后面所得到的结果中需要的术语和标号，以及引理，并且给出已知的一系列结果。第3章，主要得出：判断有向图具有Hamilton路的度充分条件，其中包括严格有向二部图具有Hamilton路的度充分条件，一般有向图具有Hamilton路的度充分条件；判断有向图为Hamilton图的度充分条件，其中包括严格有向二部图为Hamilton图的度充分条件，正则有向图为Hamilton图的度充分条件。最后，对有向图的这两个方面进行了独立性分析以及对这两方面的联系进行了论述。第4章，利用代数学的有关知识，对有向图的邻接矩阵进行分析，得出有向图具有有向Hamilton路的充分条件，必要条件，充要条件；得出有向图为有向Hamilton图的充分条件，必要条件，充要条件。最后，对这两方面的联系进行了论述。第5章，对前面所论述的内容进行了总结，并提出今后需要对有向图做进一步的讨论，进一步在上述所研究的基础上提出猜想。更多还原

【Abstract】 In this paper, the Hamiltonian qualities in Digraph are studied. On the basis of two new sufficient conditions brought up by Jorgen Bang-Jensen[7] that Digraph would be directed Hamiltonian graph and a sufficient and essential condition brought up by an associate professor Xu Shangjin[ll] that Digraph would be directed Hamiltonian graph and results of other forfathers, the sufficient conditions zbout degree of Digraph and strictly directed Bipartite graph with directed Hamiltonian path or to be directed Hamiltonian graph are shown. Also the Hamitonian qualities in Digraph are shown by making use of Adjacent matrix of Digraph. Finally the correspondent proofs are shown by uae of the correspondent contents of Graph Theory and Algebra. In the first chapter, digraph and correspondent results of Hamiltonian qualities in digraph are shown. In this paper, the studied process and correspondent results are indicated in detail. In the second chapter, technical terms and signs, lemmas and a series of known results in following Chapters are shown. In the third chapter, the following results are obtained. The sufficient conditions about degree of Digraph with directed Hamiltonian path are given (The results include strictly directed Bipartite graph with Hamiltonian path and general digraph with Hamiltonian path). The sufficient conditions about degree of Digraph to be directed Hamiltonian graph are given (The results include strictly directed Bipartite graph to be Hamiltonian graph and regular digraph to be Hamiltonian graph). Finally, the independent analyses and the connections of the two aspects of digraph is discussed. In the forth chapter, the adjacency matrices of digraphs by using Algebra are analied. The sufficient conditions,the essential conditions, the sufficient and essential conditions of Digraph with directed Hamiltonian paths or to be directed Hamiltonian graphs are obtained. Finally, the connections of the two aspects of digraph are discussed. In the fifth chapter, we sum up all the results and raise further discusses aboutdigraph in future and raise new guesses above the known results.更多还原