The Definition of Berge Graph by Incidentor Matrix

Abstract

in this work the issues of the description of a technological process performing object by a G (Y, X, H) graph are examined. The creation of any model of any technological process starts with its formal description. Any complex system can be represented by a number of interacting components. Every component is a part or a set of parts of a complex system and should have its mathematical description. Any component description can be performed in different ways in the form of a system of equations, a state machine, Petri net, a neural network, or another way. If the description of various components is performed in different ways, it will cause complications in further creation of the full formal description of a complex system. The authors have developed a mathematical apparatus which is divided in five stages. In this work the first two steps are examined - the representation of the functioning of the components of a complex system by a 1-directed graph - Berge graph and its representation by an incidentor matrix.