An elementary application of Euler’s Formula (see [@west]) gives the following.

If $G$ is a planar graph with girth $g$ then $\operatorname{mad}(G) < \frac{2g}{g-2}$. \[prop:mad\]

Theorem \[thm:Hoc\] and Proposition \[prop:mad\] yield the following corollary.

Let $G$ be a subcubic planar graph with girth $g$.

1.  If $g \geq 14$, then ${\chi_{s}'(G)}\leq 6$.

2.  If $g \geq 10$, then ${\chi_{s}'(G)}\leq 7$.

3.  If $g \geq 8$, then ${\chi_{s}'(G)}\leq 8$.

Note that no non-trivial sparsity condition on a graph $G$ with maximum degree $d$ will guarantee that ${\chi_{s}'(G)}< 2d - 1$ since any graph having two adjacent vertices of degree $d$ requires at least $2d-1$ colors to strongly edge-color the graph. We give sparsity conditions that imply a subcubic planar graph has strong chromatic index at most five and a subquartic planar graph has strong chromatic index at most seven. Previous work in this direction was initiated by Borodin and Ivanova [@BI], Chang, Montassier, Pěcher, and Raspaud [@CMPR], and most recently extended by Wang and Zhao [@WZ]. The current-best bounds are given by the following two results.

\[thm:bi\] Let $G$ be a subcubic graph.

1.  If $G$ has girth at least $9$ and $\operatorname{mad}(G) < 2 + \frac{2}{23}$, then $\chi_s'(G) \leq 5$.

