Antimagic valuations for the special class of plane graphs

Abstract

We deal with the problem of labeling the vertices, edges and faces of a special class of plane graphs with 3-sided internal faces in such a way that the label of a face and the labels of the vertices and edges surrounding that face all together add up to the weight of that face. These face weights then form an arithmetic progression with common difference d. © Springer-Verlag Berlin Heidelberg 2005.