Advancing Graph Theory with Genetic Algorithms: AFocus on Non-Inclusive Vertex Irregular Labeling

Abstract

Non-inclusive irregular vertex labeling is a labeling on a graph where the vertex labels are real numbers with weights. The weight is defined as the sum of the labels of the connected nodes. The main problem in labeling graphs is finding the formula to apply the required labeling rules. To find this formula, researchers must try to label various kinds of graphs to find labeling patterns. A Heuristic Algorithm is an algorithm that can always provide solutions and is approximate. One type of heuristic algorithm is a genetic algorithm, where this algorithm will generate random numbers as candidate solutions and after going through several selection, evolution, and evaluation processes the most appropriate value for the solution will be found. This research discusses the implementation of a genetic algorithm to label graphs (all types of graphs) in a computerized manner based on non-inclusive irregular labeling. It is hoped that this program will help researchers find non-inclusive irregular labeling formulas, without having to label graphs manually.