  Let $G$ be a graph with vertex set V and edge set E such that |V| = p and |E|
= q. For integers k\geq 0, define an edge labeling f : E \rightarrow
\{k,k+1,....,k+q-1\} and define the vertex sum for a vertex $v$ as the sum of
the labels of the edges incident to v. If such an edge labeling induces a
vertex labeling in which every vertex has a constant vertex sum (mod p), then G
is said to be k-edge magic (k-EM). In this paper, we (i) show that all the
maximal outerplanar graphs of order p = 4; 5; 7 are k-EM if and only if k\equiv
2 (mod p); (ii) obtain all the maximal outerplanar graphs that are k-EM for k =
3; 4; and (iii) characterize all (p; p-h)-graph that are k-EM for h\geq 0. We
conjecture that all maximal outerplanar graphs of prime order p are k-EM if and
only if k \equiv 2 (mod p).
