  A signed graph is a graph in which each edge is labeled with $+1$ or $-1$. A
(proper) vertex coloring of a signed graph is a mapping $\f$ that assigns to
each vertex $v\in V(G)$ a color $\f(v)\in \mz$ such that every edge $vw$ of $G$
satisfies $\f(v)\not= \sg(vw)\f(w)$, where $\sg(vw)$ is the sign of the edge
$vw$. For an integer $h\geq 0$, let $\Ga_{2h}=\{\pm1,\pm2, \ldots, \pm h\}$ and
$\Ga_{2h+1}=\Ga_{2h} \cup \{0\}$. Following \cite{MaRS2015}, the signed
chromatic number $\scn(G)$ of $G$ is the least integer $k$ such that $G$ admits
a vertex coloring $\f$ with ${\rm im}(\f)\subseteq \Ga_k$. As proved in
\cite{MaRS2015}, every signed graph $G$ satisfies $\scn(G)\leq \De(G)+1$ and
there are three types of signed connected simple graphs for which equality
holds. We will extend this Brooks' type result by considering graphs having
multiple edges. We will also proof a list version of this result by
characterizing degree choosable signed graphs. Furthermore, we will establish
some basic facts about color critical signed graphs.
