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Magic labelings of regular graphsFourth paper on VMT labelings. General recursive construction of (s,1)-VAMT labelings for any regular graph and VMT labelings for certain regular graphs. AbstractLet G(V,E) be a graph and λ be 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 say λ is a vertex magic total (VMT) labeling of G if the weight of each vertex is constant. We say λ is an (s,d)-vertex antimagic total (VAMT) 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 VAMT labelings of any even-regular graphs and VMT labelings of certain regular graphs. Status
Published in AKCE International Journal of Graphs and Combinatorics (AKCE).
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