On d-antimagic labelings of plane graphs
Martin Bača, Ljiljana Branković, Marcela Lascśaková, Oudone Phanalasy, Andrea Semaničová–Feňovčíková · Electronic Journal of Graph Theory and Applications · 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.