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Magic Labelings of Regular GraphsTalk on SEMINARIUM Matematyka Dyskretna. AbstractA vertex-magic total (VMT) labeling of a graph G(V,E) is defined as one-to-one 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 one-to-one 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 K2 and 2K3 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 2-regular factors and on Kotzig arrays. Talk given atTalk given at the SEMINARIUM Matematyka Dyskretna, AVG, Krakow, 26th April 2005.
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