VERTEX LABELINGS AND COLORINGS OF GRAPHS

In this survey we first give a brief summary on labelings and colorings on graphs in general and we present the most well known cases. Then we concentrate in the specific cases of graceful labelings and harmonious and complete colorings. We present some of the most interesting results that appeared in the literature and we also try to give some insight by presenting methods that have been used in the past. Furthermore we support our choice for studying these particular kinds of labelings and colorings by presenting several potential applications.