Labelings of plane graphs containing Hamilton path

Abstract

<p>This paper deals with the problem of labeling the vertices, edges and faces of a plane graph. A weight of a face is the sum of the label of a face and the labels of the vertices and edges surrounding that face. In a super d-antimagic labeling the vertices receive the smallest labels and the weights of all s-sided faces constitute an arithmetic progression of difference d, for each s appearing in the graph. The paper examines the existence of such labelings for plane graphs containing a special Hamilton path.</p>