Abstract
A vertex-magic total labeling of a graph G( V, E) is a one-to-one map λ from E∪ V onto the integers {1,2,…,| E|+| V|} such that λ(x)+∑λ(xy), where the sum is over all vertices y adjacent to x, is a constant, independent of the choice of vertex x. In this paper we examine the existence of vertex-magic total labelings of trees and forests. The situation is quite different from the conjectured behavior of edge-magic total labelings of these graphs. We pay special attention to the case of so-called galaxies, forests in which every component tree is a star.
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