{"paper":{"title":"A generalization on spectral extrema of $K_{s,t}$-minor free graphs","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Yanting Zhang, ZhenZhen Lou","submitted_at":"2022-11-21T01:29:15Z","abstract_excerpt":"The spectral extrema problems on forbidding minors have aroused wide attention. Very recently, Zhai and Lin [J. Combin. Theory Ser. B 157 (2022) 184--215] determined the extremal graph with maximum adjacency spectral radius among all $K_{s,t}$-minor free graphs of sufficiently large order. The matrix $A_{\\alpha}(G)$ is a generalization of the adjacency matrix $A(G)$, which is defined by Nikiforov \\cite{Nikiforov2} as $$A_{\\alpha}(G) = \\alpha D(G) + (1 - \\alpha)A(G),$$ where $0\\leq\\alpha \\leq1$. Given a graph $F$, the $A_\\alpha$-spectral extrema problem is to determine the maximum spectral radi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.11142","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/2211.11142/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"}