{"paper":{"title":"Generalized Paley graphs equienergetic with their complements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Denis E. Videla, Ricardo A. Podest\\'a","submitted_at":"2022-04-18T18:43:37Z","abstract_excerpt":"We consider generalized Paley graphs $\\Gamma(k,q)$, generalized Paley sum graphs $\\Gamma^+(k,q)$, and their corresponding complements $\\bar \\Gamma(k,q)$ and $\\bar \\Gamma^+(k,q)$, for $k=3,4$. Denote by $\\Gamma = \\Gamma^*(k,q)$ either $\\Gamma(k,q)$ or $\\Gamma^+(k,q)$. We compute the spectra of $\\Gamma(3,q)$ and $\\Gamma(4,q)$ and from them we obtain the spectra of $\\Gamma^+(3,q)$ and $\\Gamma^+(4,q)$ also. Then we show that, in the non-semiprimitive case, the spectrum of $\\Gamma(3,p^{3\\ell})$ and $\\Gamma(4,p^{4\\ell})$ with $p$ prime can be recursively obtained, under certain arithmetic conditions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2204.08509","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2204.08509/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}