#### 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*) + Σ 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.

## Comments

Published in

Discrete Mathematics, 26(1-3), 285-298.