  Let $G=(V,E)$ be an $n$-vertex graph with $m$ edges. A function $f : V \cup E
\rightarrow \{1, \ldots, n+m\}$ is an edge-magic labeling of $G$ if $f$ is
bijective and, for some integer $k$, we have $f(u)+f(v)+f(uv) = k$ for every
edge $uv \in E$. Furthermore, if $f(V) = \{1, \ldots, n\}$, then we say that
$f$ is a super edge-magic labeling. A constellation, which is a collection of
stars, is symmetric if the number of stars of each size is even except for at
most one size. We prove that every symmetric constellation with an odd number
of stars admits a super edge-magic labeling. We say that a caterpillar is of
type $(r,s)$ if $r$ and $s$ are the sizes of its parts, where $r \leq s$. We
also prove that every collection with an odd number of same-type caterpillars
admits an edge-magic labeling.
