A complete solution to the Cvetković–Rowlinson conjecture.

In 1990, Cvetković and Rowlinson conjectured that among all outerplanar graphs on n vertices, K1∨Pn−1 attains the maximum spectral radius. In 2017, Tait and Tobin confirmed the conjecture for sufficientlty large values of n. In this article, we show the conjecture is true for all n≥2 except for n=6. [ABSTRACT FROM AUTHOR]