On the spectral characterization of pineapple graphs

The pineapple graph K-p(q) is obtained by appending q pendant edges to a vertex of a complete graph K-p (q >= 1, p >= 3). Zhang and Zhang (2009) [7] claim that the pineapple graphs are determined by their adjacency spectrum. We show that their claim is false by constructing graphs which are cospectral and non-isomorphic with K-p(q), for every p >= 4 and various values of q. In addition we prove that the claim is true if q = 2, and refer to the literature for q = 1, p = 3, and (p, q) = (4,3). (C) 2016 Elsevier Inc. All rights reserved.