Study and application of graph theory in decision making in engineering problems

Abstract

This paper is one of the directions of scientific research on the application of the method of graphical representation of technical and organizational systems. The paper analyses the application of graph theory in engineering problems. The graph theory finds application in many industries, for example: in computer science, programming, communication and transport systems, economics, engineering graphics, logistics. The concept of a cycle (contour, path) in an oriented graph is introduced, and the application of graph theory to a number of transport problems is also shown. Wide application of graph theory provides also the study of network graph of reliability of prototype product creation in engineering graphics and mechanical engineering. The network graph from the point of view of graph theory is a directed graph, the vertices of which are the events of the network graph and the arcs - its work. The graph theory is also used in the construction of intermediate positions of the working zone of a quarry. In these tasks a three-dimensional graph of multivariate development of mining operations in the quarry G(EG)=G(EN) is formed from the obtained indicators. The graph theory based on topological principles can be successfully applied in open-pit mining operations to solve a number of transport problems, such as the minimum cost, the shortest path and the capacity of the exit system for various types of quarry transport, etc. The graph theory can be used for the solution of a number of transport problems.