
Magic Labelings of Odd Regular GraphsTalk on the conference IWOGL 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 oddregular graphs with a perfect matching. Talk given atTalk given at the conference IWOGL 2005, Third International Workshop on Graph Labelings, July 3 to July 7 2005, Herµany, Slovakia (4th July 2005).
