Ohodnocení kubických grafů

Abstract

In this bachelor thesis the known results of selected magic graph labelings for cubic graphs are compiled. We focus our search to Supermagic labeling, Edge magic total labeling and Vertex magic total labeling. We demonstrate specific properties of named labelings by including basic calculations and proofs of known properties. For each labeling we present summary of known results for cubic graphs along with constructions of labelings for those graphs that are magic and proofs for those graphs, that do not have these magic labelings. We also look for relations between edge coloring of cubic graphs and existence of the labeling. In the course of this work we observe, if the planarity of a graph relates to the existence (or non-existence) of the labeling. As a result we present an overview of cubic graphs for which the existence or non-existence of the selected labelings is not known.