Researches On Some Problems Of Graph Theory And Neural Networks

Graph theory and neural networks are important parts of circuits and systems. In this dissertation several problems of graph theory'and neural networks are mainly studied. It consists of seven chapters. In chapter 1, some introductive materials are presented, including research background and significance of this dissertation with the history and current status, the main contents of the paper and the list of the results obtained by the author. In chapter 2, some necessary notations of graph theory are introduced. This chapter mainly studies covered problem of one kind of special branch factor which consists of matching set and cycles. In chapter 3, orthogonal factorizations of graphs, including [0,k1]m -factorizations orthogonal to a subgraph and orthogonal factorizations of bipartite graphs, is mainly studied. In chapter 4, the dynamic behavior of asymmetric discrete Hopfield neural networks and asymmetric discrete Hopfield neural networks with delay are primarily investigated. Firstly, by defining the energy function, the stability of the networks is studied in parallel, in serial and in partially parallel updating mode, respectively. Furthermore, the conditions ensuring stability, limit cyclies and instability are obtained. Secondly, the notation of state graph of networks is presented, and the stability of the networks is studied by using the method of graph theory. In chapter 5, both the convergence of discrete time cellular neural networks with the non-reciprocal templates in interacting updating mode, in non-interacting updating mode, and some properties of strict networks with value of zero threshold are studied. In chapter 6. the asymptotical stability for asymmetric discrete time recurrent neural networks is investigated. Finally in chapter 7. the conclusion of the dissertation is drawn with some problems to be solved in graph theory and neural networks pointed out by the author. The obtained results on factors of graph are important. For the studies of discrete neural networks, some conclusions are obtained. The results here not only generalize the existing results, but also provide a theoretical foundation of performance analysis and new applications of discrete neural networks.