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Let \( G \) be a \( (p,q) \)-graph in which the edges are labeled \( 1, 2, 3, \ldots, q \). The vertex sum for a vertex \( v \) is the sum of the labels of the incident edges at \( v \). If \( G \) can be labeled so that the vertex sums are distinct, mod \( p \), then \( G \) is said to be edge-graceful. If the edges of \( G \) can be labeled \( 1, 2, 3, \ldots, q \) so that the vertex sums are constant, mod \( p \), then \( G \) is said to be edge-magic. It is conjectured by Lee [9] that any connected simple \( (p,q) \)-graph with \( q(q+1) \equiv p(p-1)/2 \pmod{p} \) vertices is edge-graceful. We show that the conjecture is true for maximal outerplanar graphs. We also completely determine the edge-magic maximal outerplanar graphs.