The Study of Some Existing and New Graph Labeling Techniques

Abstract

Graph theory is a branch of Mathematics which can be used as a tool to solve variety of problems. Graph theory has multi faced applications in various fields. Many real life problems can be converted in to a graph theory problem and can be solved using applied properties of graphs to them. Our study is on graph labeling problems which is one of the mainly rising research area of graph theory recently. newlineGraph labeling is a part of graph theory introduced by A. Rosa. Graph labeling is one of the mainly rising area of Mathematics which project integers vertices edges both subject definite setting. Labels are a kind of naming that can be applied to any node in the graph. In the mathematical discipline of graph theory, a graph labeling is the assignment of labels, traditionally represented by integers, to edges and/or vertices of a graph. Graphs are used to present data. Adding labels to your graph helps provide important information about what the data in your graph represents. Labeled graphs serves as useful models for a broad range of applications in various fields. The concept of graph labelling is the interesting field of research in the current area for many researchers. newlineIn this research the graphs considered are finite, simple and undirected. and#119866;=(and#119881;,and#119864;) denotes a graph with vertex set and#119881; and edge set and#119864;. We have worked on different types of labelings and have derived new results for various graphs. Some of the labelings are already in existence and some are newly added by us which are skolem difference mean labeling, extra skolem difference mean labeling, skolem minkowski-4 mean labeling, edge magic total and edge trimagic total labeling, cube square difference labeling, difference perfect square cordial labeling. The main purpose of this research work is to provide new ideas to gain knowledge in the area of graph labeling. The study of different graph labeling techniques, may help to link between graph labeling and other various fields which can be a good source of research.