Magic Labeling of Cycle Like Graphs

Abstract

Graph labeling is play very vital role in graph theory applications like network addressing of communication, X-ray, circuit designing, crystallography, radar, missile guidance, astronomy and data base management.

A labeling is bijective mapping in which natural number are assigned to vertices or edges. If weights of all vertex have same sum, such labeling is called magic labeling. The notion of (a, d) vertex-antimagic-total labeling was introduced by Baca et al. [5] in 2000. A labeling in which domain set consists of all vertices and edges is called total labeling. A labeling is called super (a, d)-vertex antimagic-total labeling (VAMTL) if we allot smallest number to vertices and then to edges. Hussain et al. [17, 18] formulated (a,d)-vertex antimagic total labeling on Harary graphs, however, many cases are still open.

This dissertation learning about the configuration of new results of vertex-magic total labeling and (a,d)-vertex antimagic total (VAT) labeling of Harary graphs. Also we construct same new results of super (a, d)-vertex antimagic total (VAT) labeling on Harary graphs.