DDM ohodnocení orientovaných grafů

Abstract

This thesis studies difference distance magic (DDM) labeling of oriented graphs, with a focus on orientations of k-regular simple graphs. The aim is to investigate the existence of such labelings for various classes of graph orientations, with particular emphasis on their dependence on the order of the graph. The main result is a complete classification of the orders for which orientations of 4-regular simple graphs admit a DDM labeling, even within the class of weakly connected graphs. Furthermore, partial classifications of some orders according to their modularity are obtained for orientations of 3-regular simple graphs, as well as a partial classification of orders of 2m-regular simple graphs for m ≥2.