On d-antimagic labelings of plane graphs - Martin Baca; Ljiljana Brankovic; Marcela Lascsakova; Oudone Phanalasy; Andrea Semanicova-Fenovciova (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2013)
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.