The Theory Of The Tenacity Of Network Systems With Application To Marine Engineering

To Observe and ponder the systems existing in the practical world one can often encounter with the problems of specific relations among the objects concerned .The knowledge of graph theory can be used in solving the related problems after the relations between these objects are described with graph and made into models. The marine engineering system is a very complicated system, it concerns not only with the relationship among seafares, but also the relationship between man and machine equipment, and between machine equipment and apparatus. These relationships can be clarified with the knowledge of the connectivity or reliability of network. Thispaper studies an important parameter of network connectivity— the theory oftenacity and its application to the marine engineering management systems. The main results are as follows:(1) Study and obtain some special tenacity such as complete graph, star graph, complete bipartite graph, grids and torl of complete graph, the range of value of the tenacity, the structures of the tenacity and network graph and the relationship between the structures of the maximum and minimum tenacity.(2) With the basic theory of the tenacity, give the optimal design procedures, describe the maximum and minimum network graph structures which the network graph may have under the given conditions of network graph main parameters and the tenacity, and establish the structural methods of these structures. These results can be well used in the human relationship in the marine engineering systems and information exchange systems.(3)Harary graph plays a very important role in the optimal design of reliability communication network. The tenacity of Harary graph is calculated from the basic theory of the tenacity.(4) By using the definitions of the parameters of connectivity, toughness, coretivity and integrity, the thesis compares the differences between the tenacity and theparameters in connectivity, hence concluding that tenacity is a fairly good invariant in describing connectivity of graph as a whole.(5) Further, the range of value of the edge tenacity on the basis ofthe tenacity, edge tenacity of some special graphs, edge toughness and the relationship between the edge integrity are investing.(6) The conjecture related to strict edge tenacious graph is solved, and a necessary and sufficient condition of discrimination the strict edge tenacious graph is obtained, the resuts published in an international journal.(7) The human relationship in the marine engineering system is analyzed by using the optimal design theory of the tenacity . The main question in social psychology is the study of human relationship ,and one of the main contents of studying human relationship is the study of the group human relationship. The staff in the marine engineering system is a very special small group. Studying this small group by the theory of the tenacity, inproving and broadening what the predecessors have done in this field give a new method of discriminating whether the human relationship is good or not in a small group. The problems of optimal design in human relationship under different conditions are also discussed.(8) We analyze and study the marine engineering management information exchange network system by using the optimal theory of the tenacity, obtain a method of analyzing whether the marine engineing management information exchange system is good or bad such as the transmitting speed of information and the accuracy of transmission, and discuss the structures of the optimum information exchange networks. These studies are initiative in our country and advanced in the international society. The theories, the algorithms and the models in this paper can also be used conveniently in the economic system, the military network system, conmunication network system and other fields.