{"paper":{"title":"Connected components and non-bipartiteness of generalized Paley graphs","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":"2024-09-30T23:23:46Z","abstract_excerpt":"In this work we consider the class of Cayley graphs known as generalized Paley graphs (GP-graphs for short) given by $\\Gamma(k,q) = Cay(\\mathbb{F}_q, \\{x^k : x\\in \\mathbb{F}_q^* \\})$, where $\\mathbb{F}_q$ is a finite field with $q$ elements, both in the directed and undirected case. Hence $q=p^m$ with $p$ prime, $m\\in \\mathbb{N}$ and one can assume that $k\\mid q-1$. We first give the connected components of an arbitrary GP-graph. We show that these components are smaller GP-graphs all isomorphic to each other (generalizing a Lim and Praeger's result from 2009 to the directed case). We then cha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.00281","kind":"arxiv","version":4},"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/2410.00281/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"}