$d$-Antimagic Labelings of Plane Graphs $P_a^b$

Abstract

We refer to a labeling of a plane graph as a $d$-antimagic labeling if the vertices, edges, and faces of the graph are labeled in such a way that the label of a face and the labels of the vertices and edges surrounding that face add up to a weight of that face and the weights of all the faces form an arithmetic progression of difference $d$. This paper describes $d$-antimagic labelings for a special class of plane graphs.