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Labelings of plane graphs containing Hamilton path

Abstract:

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. © 2011 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.