{"paper":{"title":"Sharp upper bounds on the $A_\\alpha$-spectral radius of graphs","license":"http://creativecommons.org/licenses/by-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Zheng-Jiang Xia, Zhen-Mu Hong, Zhi Qiao","submitted_at":"2026-05-30T18:33:11Z","abstract_excerpt":"Let $G$ be a simple graph with degree diagonal matrix $D(G)$ and adjacency matrix $A(G)$. The signless Laplacian matrix of $G$ is defined as $Q(G)=D(G)+A(G)$. For a real number $\\alpha \\in [0, 1]$, Nikiforov (2017) proposed the $A_\\alpha$-matrix of a graph $G$ as $A_{\\alpha}(G)=\\alpha D(G)+(1-\\alpha)A(G)$. The $A_\\alpha$-spectral radius of $G$, denoted by $\\rho_\\alpha(G)$, is the largest eigenvalue of $A_\\alpha(G)$, where $\\rho_0(G)=\\rho(G)$ is the spectral radius of $A(G)$ and $2\\rho_{\\frac{1}{2}}(G)=q(G)$ is the spectral radius of $Q(G)$. Sun and Das (2020) proved that for any non-isolated v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.00843","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/2606.00843/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"}