Some results about super edge-magic and (k, d)-arithmetic graphs and labelings

Abstract

The work in this paper can be divided into two parts. One part deals with the (k,d)-arithmetic properties of graphs which are locally dense; that is to say, with a large clique in comparison to their size. The other part deals with finding upper bounds for the difference, in absolute value, between the biggest and the smallest labels that can be used in a (k, d)-arithmetic labeling. We show that while in some cases such a difference cannot exceed a certain value, in other cases it is unbounded.