# Strong Edge-Magic Graphs of Maximum Size

MacDougall, James A. and Wallis, W. D. (2008) Strong Edge-Magic Graphs of Maximum Size. Discrete Mathematics, 308 . pp. 2756-2763.

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An {\em edge-magic total labeling} on G is a one-to-one map $\lambda$ from $V (G) \cup E(G)$ onto the integers 1, 2, . . . , $|V (G) \cup E(G)|$ with the property that, given any edge $(x, y), \lambda(x) + \lambda(x, y) + \lambda(y) = k$ for some constant $k$. The labeling is {\em strong} if all the smallest labels are assigned to the vertices. Enomoto et al. proved that a graph admitting a strong labeling can have at most $2|V (G)| − 3$ edges. In this paper we study graphs of this maximum size.