Martin Baca, Ljiljana Brankovic, Marcela Lascsakova, Oudone Phanalasy, Andrea Semanicova-Fenovciova
Abstract
The paper deals with the problem of labeling the vertices and edges of a plane graph in such a way that the labels of the vertices and edges surrounding that face add up to a weight of that face. A labeling of a plane graph is called d-antimagic if for every positive integer s, the s-sided face weights form an arithmetic progression with a difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In the paper we examine the existence of such labelings for several families of plane graphs.
Keywords
plane graph, d-antimagic labeling, super d-antimagic labeling
