Author/Authors :
Bača, Martin Technical University - Department of Applied Mathematics and Informatics, Slovakia , Brankovic, Ljiljana University of Newcatle - School of Electrical Engineering and Computer Science, Australia , Lascsáková, Marcela Technical University - Department of Applied Mathematics and Informatics, Slovakia , Phanalasy, Oudone National University of Laos - Department of Mathematics, Laos , Semaničová–Feňovčíková, Andrea Technical University - Department of Applied Mathematics and Informatics, Slovakia
Abstract :
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 d-antimagic if for every positive integer s, the s-sided face weights form an arithmetic progression with a difference d. Such a labeling is called super if the smallest possible labels appear on the vertices. In the paper we examine the existence of such labelings for several families of plane graphs.
Keywords :
plane graph , d , antimagic labeling , super d , antimagic labeling
