  A \textit{subtractive arc-magic labeling} (SAML) of a directed graph
$G=(V,A)$ is a bijection $\lambda :V\cup A \to \{1,2,\ldots,|V|+|A|\}$ with the
property that for every $xy\in A$ we have $\lambda(xy)+\lambda(y)-\lambda(x)$
equals to an integer constant. If $\lambda(xy)+\lambda(y)-\lambda(x)$ are
distinct for every $xy\in A$, then $\lambda$ is a \textit{subtractive
arc-antimagic labeling} (SAAL). A \textit{subtractive vertex-magic labeling}
(SVML) of $G$ is such bijection with the property that for every $x\in V$ we
have $\lambda(x)+\sum_{y\in V, yx \in A} \lambda(yx)-\sum_{y\in V, xy\in A}
\lambda(xy)$ equals to an integer constant. If $\lambda(x)+\sum_{y\in V, yx \in
A} \lambda(yx)-\sum_{y\in V, xy\in A} \lambda(xy)$ are distinct for every $x\in
V$, then $\lambda$ is a \textit{subtractive vertex-antimagic labeling} (SVAL).
In this paper we prove some existence or non-existence of SAML, SVML, SAAL, and
SVAL for several basic families of directed graphs, such as paths, cycles,
stars, wheels, tadpoles, friendship graphs, and general butterfly graphs. The
constructions are given when such labeling(s) exists.
