{"paper":{"title":"On the spectral characterization of pineapple graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hatice Topcu, Sezer Sorgun, Willem H. Haemers","submitted_at":"2015-11-27T13:57:10Z","abstract_excerpt":"The pineapple graph $K_p^q$ is obtained by appending $q$ pendant edges to a vertex of a complete graph $K_{p}$ ($q\\geq 1,\\ p\\geq 3$). 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 $q$. 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,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.08674","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}