{"paper":{"title":"A classification of all 1-Salem graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"James McKee, Lee Gumbrell","submitted_at":"2011-09-28T17:22:01Z","abstract_excerpt":"One way to study certain classes of polynomials is by considering examples that are attached to combinatorial objects. Any graph $G$ has an associated reciprocal polynomial $R_G$, and with two particular classes of reciprocal polynomials in mind one can ask the questions: (a) when is $R_G$ a product of cyclotomic polynomials (giving the cyclotomic graphs)? (b) when does $R_G$ have the minimal polynomial of a Salem number as its only non-cyclotomic factor (the non-trival Salem graphs)? Cyclotomic graphs were classified by Smith in 1970. Salem graphs are `spectrally close' to being cyclotomic, i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.6275","kind":"arxiv","version":2},"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"}