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Magic labelings of regular graphs

Fourth paper on VMT labelings. General recursive construction of (s,1)-VAMT labelings for any regular graph and VMT labelings for certain regular graphs.

Abstract

Let 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).
P. Kovář Magic labelings of regular graphs, AKCE International Journal of Graphs and Combinatorics, vol. 2007/4, 3, 261-275, (2007)


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Last update: 29.12.2011