On the maximum spectral radius of planar graphs

Abstract

This paper investigates the maximum spectral radius of planar graphs with concrete fixed number of vertices, providing some tight bounds on the maximum spectral radius of general planar graph resorting to its order, and confirming that among all planar graphs containing dominating vertex with concrete fixed order $n\ge 48$, the join of $P_2$ and $P_{n-2}$ attains the maximum spectral radius.