USING ELEMENTS OF GRAPH THEORY TO SOLVE TYPICAL PROBLEMS

Abstract

This article discusses the fundamental concepts of graph theory and the solution of typical problems through the application of its elements. The practical significance of graph models is especially evident in the planning and optimization of transport systems, the study of computer and social networks, the modeling of biological and engineering structures, data analysis, and resource allocation. Graph theory makes it possible to visualize connections between objects and the structure of these connections, which allows a deeper understanding and more effective problem solving. The article provides a detailed analysis of shortest path algorithms, Eulerian and Hamiltonian cycles, the construction of a minimum spanning tree, and graph coloring problems. In addition, the potential applications of graph theory algorithms to practical tasks are discussed, with examples and explanations of the specific features of each method. In conclusion, it is shown that graph theory is widely and effectively applied in education, scientific research, technological development, and everyday practice. This material helps students and researchers to better understand the concepts of graph theory, model problems, and develop comprehensive solutions.