  Let $G$ be an simple graph of order $n$ whose adjacency eigenvalues are
$\lambda_1\ge\dots\ge\lambda_n$. The HL--index of $G$ is defined to be $R(G)=
\max\{|\lambda_{h}|, |\lambda_{l}|\}$ with
$h=\left\lfloor\frac{n+1}{2}\right\rfloor$ and $
l=\left\lceil\frac{n+1}{2}\right\rceil.$ Mohar conjectured that $R(G)\le 1$ for
every planar subcubic graph $G$. In this note, we prove that Mohar's Conjecture
holds for every $K_4$-minor-free subcubic graph. Note that a $K_4$-minor-free
graph is also called a series--parallel graph. In addition, $R(G)\le 1$ for
every subcubic graph $G$ which contains a subgraph $K_{2,3}$.
