Theoretical foundations to apply graph theory in the innovative approach implementation to enterprise development

The paper is devoted to the theoretical substantiation of the possibility and expediency of applying graph theory in the optimization of innovation activities carried out by enterprises in the real sector in the process of introducing digital technologies. The purpose of the study is to prove the feasibility of using graph theory when optimizing the process of implementing an innovative project to introduce digital technologies at enterprises in the real sector. Research objectives: systematization of the experience of applying graph theory in solving economic and managerial problems; determining the types of graphs for modeling the management process at an enterprise in the real sector; determining the applicability of graphs for modeling the process of implementing an innovative project based on the choice of the optimal path. Research methods: a set of analytical and system methods and related tools related to graph theory, peer review and modeling. Based on the authors' analysis of the application of the basic concepts and algorithms of graph theory in modeling both various production processes, including the stages of design and design and production management, and the activities of the enterprise as a whole, the possibility of using graphs in the implementation of digital technologies as part of the implementation of an innovative project is substantiated. The study considers the process of constructing a graph, in which the vertices are the carriers of competencies, and the arcs are the process of action, which requires a certain set of resources to perform. This representation is expressed as a mathematical object in the form of a set of two sets. The presented interpretation of weighted directed graphs can be a subgraph of a larger graph, which is an innovation system. According to the results of the study, the rationality and expediency of using graph theory for modeling managerial decisions in general is noted. At the same time, the considered model can be applicable to characterize the process of introducing digital technologies into the activities of an enterprise in the real sector, taking into account the given optimization objective function.