FULL ENUMERATION METHODS ON GRAPHS

Abstract

Requirements for algorithms for specific problems of discrete mathematics are changing. This is dictated by an urgent need to increase calculation accuracy in technology-related problems brought about by rapid digitization and virtualization, which actively permeated various scientific areas and changes the approach to previously studied objects. These objects include n-dimensional structures, known as circular structures, that describe global processes occurring in communication networks, multi-processor systems, in collective communications, stock market structures etc. Given that, both the development of new mathematical methods of solving problems and the solution of related calculation problems are deemed important. The enumeration method, based on various modifications of systematic viewing (traversal) of graph elements and labeling, has been widely used and quite fully developed for a long time. The purpose of the article is to announce graphs presentation and the enumeration methods on graphs presentations: the transposition method and the node-graph method. This publication presents the basic results of the author's work on reducing the severity of the NP-complete problem class.