Discrete Mathematics and Combinatorics Commons^™

Distance Magic-Type And Distance Antimagic-Type Labelings Of Graphs, Bryan Freyberg

Dissertations, Master's Theses and Master's Reports

Generally speaking, a distance magic-type labeling of a graph G of order n is a bijection f from the vertex set of the graph to the first n natural numbers or to the elements of a group of order n, with the property that the weight of each vertex is the same. The weight of a vertex x is defined as the sum (or appropriate group operation) of all the labels of vertices adjacent to x. If instead we require that all weights differ, then we refer to the labeling as a distance antimagic-type labeling. This idea can be generalized …