Cvetković–Rowlinson outerplanar spectral-radius conjecture

Let $n$ be the number of vertices, let $P_{n-1}$ be the path on $n-1$ vertices, and let $\vee$ denote the join of graphs. Cvetković–Rowlinson's conjecture. The outerplanar graph on $n$ vertices with maximum spectral radius is

$$K_1\vee P_{n-1}.$$

The source presents this as a historical conjecture, without giving evidence of a resolution.