Sharp bounds on the spectral radius of Halin graphs and other k-outerplanar graphs

We provide upper and lower bounds on the spectral radius of Halin graphs and some other classes of k-outerplanar graphs. For both the Halin and the k-outerplanar cases we provide examples where the bounds are met, thus demonstrating sharpness. The upper bound in the Halin case, improves upon Shu et al.'s claimed bound for a very wide class of graphs. A consequence of the upper bound is a generalization that holds for all graphs and which bounds the largest eigenvalue based on a graph partition; to the best of our knowledge this result is new also.