Vertex-magic labeling of trees and forests Original Research Article

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 thatλ(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.