On Edge-magic Labelings of Forests

Abstract

Given an n-vertex graph G = (V,E) with m edges, a labeling f of V ∪ E that uses all the labels in the set {1,2,...,n + m} is edge-magic if there is an integer k such that f(u) + f(v) + f(uv) = k for every edge uv ∈ E. Furthermore, if the labels in {1,2,...,n} are given to the vertices, then f is called super edge-magic. Kotzig [On magic valuations of trichromatic graphs, Reports of the CRM, 1971] started the investigation of super edge-magic labelings of forests. Following this line of research, we prove that some forests of stars admit a super edge-magic labeling and that some forests of caterpillars admit an edge-magic labeling.