An Overview of Second- and Third-Power Gap Labeling on Combinatorial Structures

Labeling of a graph is an assignment of labels (numbers) to its vertices or/and edges or faces, which satisfy some conditions. The efforts to find solutions to many practical problems in real life situations have led to the development of several graph labeling methods - graceful, harmonius, prime, divisor, magic, antimagic, cordial, product cordial, prime cordial etc. Also, the various labeling methods generate so many new types of graphs. Graph labeling problems have three important characteristics. 1. A set of numbers from which vertex labels are chosen. 2. A rule that assigns a value to each edge. 3. A condition that these values must satisfy. A detailed survey on graph labeling is given by Gallian [10]. Vast amount of literature is available on different types of graph labeling. According to Beineke and Hegde [2] graph labeling serves as a frontier between number theory and structure of graphs.