The spectral radius of minor-free graphs

In this paper, we present a sharp upper bound for the spectral radius of an n-vertex F-minor-free graph for sufficiently large n, where F is obtained from the complete graph Kr by deleting disjoint paths. Furthermore, the graphs which achieve the sharp bound are characterized. This result may be regarded as a spectral extremal analogue of the number of edges in an n-vertex F-minor-free graph. (c) 2023 Elsevier Ltd. All rights reserved.