Graceful and Edge-Antimagic Labelings

Abstract

A graph labeling is an assignment of integers (labels) to the vertices and/or edges of a graph. Within vertex labelings, two main branches can be distinguished: difference vertex labelings that associate each edge of the graph with the difference of the labels of its endpoints. Graceful and edge-antimagic vertex labelings correspond to these branches, respectively. In this paper, we study some connections between them. Indeed, we study the conditions that allow us to transform any \(a\)-labeling (a special case of graceful labeling) of a tree into an \((a, 1)\)- and \((a, 2)\)-edge antimagic vertex labeling.