Antimagic labeling of graphs

The concept of labeling of graphs has attracted many researchers to this branch of research since the concept was introduced. It is becoming popular, partly because of mathematical challenges, and partly also because of the wide range of applications in other branches of science. A labeling of a graph is a map from one or more graphs elements to sets of numbers, for instance, labeling of edges, vertices, both edges and vertices, or edges, vertices and faces, if a labeling is applied to plane graph. Correspondingly, we distinguish edge labeling, vertex labeling, total labeling, or d-labeling. In this thesis we deal with edge labeling to contribute new results towards settling the Hartsfeld and Ringel conjecture that `Every graph different from K₂ is antimagic'. We also prove that every graph has a vertex antimagic total labeling, and an edge antimagic total labeling if the graph contains no isolated vertex. We introduce the notion of totally antimagic total labeling and provide several initial results for such a labeling. Furthermore, we study super d-antimagic labeling and obtain several new results. Nevertheless, many open problems remain in antimagic labeling of graphs and we conclude the thesis by listing some of those that arose from our study.