## Abstract

The article considers the main principles of graph dynamical systems, as well as a number of examples of the use of graph dynamical operations for simulation modeling of the organizational system structure and composition management problems. The basic concepts and definitions of the graph dynamical systems theory are given. Using the subordination function as an example, a graph is constructed with numbered vertices, each component of which is a tree. Considered the situation when initial graph is time variant and there is a sequence of graphs such that every graph of sequence is either a tree or a forest. At the ”development” of the sequence in time the unilaterally connected graph can be multiply connected graph, i.e. new roots and ”growing” trees may form. The vertex resubordination may occur inside of the tree. Each graph of this sequence corresponds to a well-defined function of subordination. As result, the sequence of alternately graphs, i.e. a graph path represented as a sequence of functions of subordination. Transition of each of the subordination functions of the path into other subordination function is carried out by performing three types of operations: unary, binary and r-ary operations. Graph dynamical modeling of organizational structure transformation with its preliminary destructuring are described. As an example of such modeling considered the task of the functioning organization restructuring, the structure of which is represented by 4-level hierarchy. Also in the paper are examples of graph and dynamic modelling of organizational structure’s members reducing.

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