A Study on Graph Labelling, Graph Coloring, their Types and Applications

Authors- Research Scholar Rouf Gulzar, Assistant Professor Priyanka Bhalero

Abstract-Graph theory is an interdisciplinary field that lies at the interface of computer science and mathematics. It studies graphs, which are engineering Structures used to model two dimensional interactions inside given objects by the method of graphical representations and mathematical derivations. The study of graph theory is applied in many fields, including biology, computer science, social sciences, and even transportation networks. Many mathematical theorems and models are proven using graph theory for correct comprehension and future study. Graph labeling is one of the main areas of graph theory. In this review paper, We examine several distinct types of graph labeling, including Graceful, Prime, Edge, Harmonious, and Graph coloring, as well as their mathematical requirements and characteristics. Additionally, we will explore some of the applications of graph labeling in important technological fields like automatic routing, communication network addressing, X-ray crystallography, and coding theory. Applications of graph theory include the creation of security keys, the segmentation of brain MRIs, the detection of tumors using cut sets, virus graphs, and their use during the COVID-19 pandemic. One of the most crucial areas for graph theory research is the assignment of color to different graph constituents. Applications in the sciences, medical sciences, computer engineering, electronics and communications, electrical engineering, network theory, artificial intelligence and machine learning, psychology, and economics are numerous. There are still a lot of unanswered questions, and mathematicians and academics from all over the world are working on it. In this study, we examine graph coloring, coloring types, graph-coloring theorems and axioms, and its applications.

DOI: /10.61463/ijset.vol.12.issue6.373