Antimagic Labelings of Generalized Petersen Graphs That are Plane

Abstract

We deal with the problem of labeling the vertices, edges, and faces of a plane graph 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 \(s\)-sided faces constitute an arithmetic progression of difference \(d\). In this paper, we describe various antimagic labelings for the generalized Petersen graph \(P(n, 2)\). The paper concludes with a conjecture.