\(d\)-Antimagic Labelings of Plane Graphs \(P_{b}^{a}\)

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.