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Zhang and Zhang [\"Some graphs determined by their spectra\", Linear Algebra and its Applications, 431 (2009) 1443-1454] 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 $p\\geq 4$ and various values of $q$. 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