Ohodnocení grafů

Abstract

In this bachelor thesis we deal with the area called graph labeling. We examine 3-regular graphs and 4-regular graphs with extended handicap labeling. We mention the current knowledge about r-regular graphs with extended handicap labeling. We provide new results, which are summarized into mathematical theorems about existence of 3-regular graphs, where the number of vertices must be a multiple of 8 and about existence of 4-regular graphs, where number of vertices must be a multiple of 12. We also describe a new polynomial algorithm for finding all r-regular graphs with extended handicap labeling.