  The packing chromatic number $\chi_{\rho}(G)$ of a graph $G$ is the smallest
integer $k$ such that there exists a $k$-vertex coloring of $G$ in which any
two vertices receiving color $i$ are at distance at least $i+1$. It is proved
that in the class of subcubic graphs the packing chromatic number is bigger
than $13$, thus answering an open problem from [Gastineau, Togni, $S$-packing
colorings of cubic graphs, Discrete Math.\ 339 (2016) 2461--2470]. In addition,
the packing chromatic number is investigated with respect to several local
operations. In particular, if $S_e(G)$ is the graph obtained from a graph $G$
by subdividing its edge $e$, then $\left\lfloor \chi_{\rho}(G)/2 \right\rfloor
+1 \le \chi_{\rho}(S_e(G)) \le \chi_{\rho}(G)+1$.
