  A dynamic coloring of the vertices of a graph $G$ starts with an initial
subset $F$ of colored vertices, with all remaining vertices being non-colored.
At each time step, a colored vertex with exactly one non-colored neighbor
forces this non-colored neighbor to be colored. The initial set $F$ is called a
forcing set of $G$ if, by iteratively applying the forcing process, every
vertex in $G$ becomes colored. The forcing number of a graph $G$, denoted by
$F(G)$, is the cardinality of a minimum forcing set of $G$. The maximum nullity
of $G$, denoted by $M(G)$, is defined to be the largest possible nullity over
all real symmetric matrices $A$ whose $a_{ij} \neq 0$ for $i \neq j$, whenever
two vertices $u_{i}$ and $u_{j}$ of $G$ are adjacent. In this paper, we
characterize all graphs $G$ of order $n$, maximum degree at most three, and
$F(G)=3$. Also we classify these graphs with their maximum nullity.
