{"paper":{"title":"Spectral extrema of graphs with fixed size: forbidden a fan graph, friendship graph or theta graph","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lantao Zou, Shuchao Li, Sishu Zhao","submitted_at":"2024-09-24T09:40:03Z","abstract_excerpt":"It is well-known that the Brualdi-Hoffman-Tur\\'an-type problem inquiries about the maximum spectral radius \\( \\lambda(G) \\) of an \\( F \\)-free graph \\( G \\) with \\( m \\) edges. Let \\( \\theta_{1,p,q} \\) denote the theta graph, which is constructed by connecting two vertices with 3 internally disjoint paths of lengths 1, \\( p \\), and \\( q \\) respectively. Let \\( F_k \\) be the fan graph, that is, the join of a \\( K_1 \\) and a path \\( P_{k - 1} \\). Let \\( F_{k,3} \\) be the friendship graph, obtained by having \\( k \\) triangles share a common vertex. In this paper, we utilize the \\( k \\)-core metho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.15918","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.15918/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"}