On d-antimagic labelings of plane graphs

Martin Baca (Department of Applied Mathematics and Informatics, Technical University, Kosice)
Ljiljana Brankovic (School of Electrical Engineering and Computer Science, The University of Newcatle)
Marcela Lascsakova (Department of Applied Mathematics and Informatics, Technical University, Kosice)
Oudone Phanalasy (Department of Mathematics, National University of Laos, Vientiane)
Andrea Semanicova-Fenovciova (Department of Applied Mathematics and Informatics, Technical University, Kosice)

Electronic Journal of Graph Theory and Applications (EJGTA)
Vol 1, No 1 (2013): Electronic Journal of Graph Theory and Applications

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.