On d-antimagic labelings of plane graphs

Abstract

<p>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 <i>d-antimagic</i> if for every positive integer s, the s-sided face weights form an arithmetic progression with a difference d. Such a labeling is called <i>super</i> if the smallest possible labels appear on the vertices.</p> <p>In the paper we examine the existence of such labelings for several families of plane graphs.</p>