Vertex-magic Labeling of Trees and Forests

Authors

I. D. Gray, University of Newcastle
J. MacDougall, University of Newcastle
John P. McSorley, Southern Illinois University CarbondaleFollow
Walter D. Wallis, Southern Illinois University Carbondale

Comments

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

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.

Recommended Citation

Gray, I. D., MacDougall, J., McSorley, John P. and Wallis, Walter D. "Vertex-magic Labeling of Trees and Forests." (Jan 2003).