Spectral radius of hamiltonian planar graphs and outerplanar graphs

The spectral radius is an important parameter of a graph related to networks. A method for estimating the spectral radius of each spanning subgraph is used to prove that the spectral radius of a Hamiltonian planar graph of order n ≥ 4 is less than or equal to
$2 +\quad \overline{3n-11}$
and the spectral radius of the outer planar graph of order n ≥ 6 is less than or equal to
$2 \quad\overline{2}+ \quad\overline{n-5}$
, which are improvements over previous results. A direction for further study is then suggested.