
Magic labelings of regular graphsTalk on the conference Graphs 2005. AbstractA vertex magic 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 weights (sums of the label of a vertex and the labels of all edges incident to this vertex) are equal to 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 recent results on VMT and VAMT labelings of certain evenregular graphs and on VMT labelings of certain oddregular graphs. Talk given atTalk given at the conference GRAFY 2005, 40th Czech and Slovak Conference of graph Theory and Combinatorics, 30th May  3rd June 2005, Budmerice, Slovakia, (3rd June 2005).
