A (p, q)-graph G = (V, E) is total edge-magic if there exists a bijection f: V ∪ E → {lcub}1, 2, …, p + q{rcub} such that ∀ e = (u, v) ∈ E, f(u) + f(e) + f(v) = constant. A total edge-magic graph is a super edge-magic graph if f(V(G)) = {lcub}1, 2, …, p{rcub}. Kotzig and Rosa showed that all caterpillars are super edge-magic. Enomoto et al. conjectured that all trees are super edge-magic. Various aspects of super edge-magic graphs are studied in this writing project. Computers are used to search for super edge-magic labelings. A computer program that verifies that all trees with less than seventeen vertices are super edge-magic is presented. Some theorems for extending a caterpillar to a super edge-magic lobster are also described.
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