Vertex Antimagic Edge Labeling of Cube of A Path Graph

Abstract

There are many concepts in science that are very hard to understand and to make use of them in a effective way, it is atmost important to have a tool that best explains these complex concepts in a simpler way. Graph theory is one of the most interesting topics in mathematics that was used to explain many complicated concepts in a simpler and easier way. Graph theory is not just about points and lines and above all, there are many interesting topics in graph theory which has motivated many scholars to pursue research in different areas. One of the most interesting and elite topics in graph theory is the path. The researchers have discovered different types of concepts using paths and have proved different characteristics. Cube of a path graphs are one of those fascinating graphs that have evolved from paths and has been proved to admit a variety of properties. Like paths, labeling is also an area where graph theoretic researchers have shown great interest and have come up with different types of labeling. With the discovery of a spate of labeling, it has motivated and kindled the researchers to apply these labeling to a variety of graphs and check the admittance of different types of properties. One such intriguing type of labeling is the vertex antimagic edge labeling. In this paper, we will show that the cube of a path graph admits vertex antimagic edge labeling.