Magic labelings of regular graphs
Petr Kovář, Joseph A. Gallian · AKCE International Journal of Graphs and Combinatorics · 2007
Let G(V,E) be a graph andbe a bijection from the set V ( E to the set of the first |V | + |E| natural numbers. The weight of a vertex is the sum of its label and the labels of all adjacent edges. We sayis a vertex magic total (VMT) labeling of G if the weight of each vertex is constant. We sayis an (s,d) -vertex antimagic total (VAT) labeling if the vertex 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. We give constructions of VAT labelings of any even-regular graphs and VMT labelings of certain regular graphs.