The Study Of The Hamiltonian Qualities In Digraph

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.