Metody konstrukcí magických ohodnocení grafů

Abstract

In this master thesis we focus on distance magic labeling, handicap labeling, k-handicap labeling, distance antimagic labeling and supermagic labeling. The known results and necessary conditions for existence of these labelings are compiled. Based on the known results, the goal was to come up with similar approaches for other labelings as well. We try to combine graphs with different labelings so that the resulting graph has one of the given labelings. We are looking for similar and different properties of the labelings, that could be a reason for existence of the labelings of the resulting graph. For supermagic labeling, we introduced the so-called spectrum of the magic constant, where we can increase all labels by the same value to get an infinite number of new supermagic labelings for one regular graph. We also came up with a proposition that allows us to use a k-dimensional magic cube as a (-k)-handicap labeling of a graph. Another outcome of this thesis is the construction of supermagic labeling of a graph, that was created by union of two supermagic graphs, by shifting the original labeling of the unified graphs. A summary is given at the end of the thesis, where we examine all the constructions used and for what kind of labeling and type of graphs these constructions can be used.