
Magic Labelings of Regular GraphsTalk on SEMINARIUM Matematyka Dyskretna. AbstractA vertexmagic total (VMT) labeling of a graph G(V,E) is defined as onetoone mapping from V ∪ E to the set of integers {1, 2, ..., V+E} with the property that the sum of the label of a vertex and the labels of all edges incident to this vertex is the same constant for all vertices of the graph. An (s,d)vertex antimagic total (VAMT) labeling of a graph G(V,E) is defined as onetoone mapping from V ∪ E to the set of integers {1, 2, ..., V+E} with the property that the weights form an arithmetic progression starting at s with difference d. J. MacDougall conjectured that any regular graph with the exception of K_{2} and 2K_{3} has a VMT labeling. In the talk we present a technique for constructing VMT and VAMT labelings of certain regular graphs based on decomposing G into 2regular factors and on Kotzig arrays. Talk given atTalk given at the SEMINARIUM Matematyka Dyskretna, AVG, Krakow, 26th April 2005.
