{"paper":{"title":"On the $\\alpha$-spectral radius of graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bo Zhou, Haiyan Guo","submitted_at":"2018-05-09T11:08:12Z","abstract_excerpt":"For $0\\le \\alpha\\le 1$, Nikiforov proposed to study the spectral properties of the family of matrices $A_{\\alpha}(G)=\\alpha D(G)+(1-\\alpha)A(G)$ of a graph $G$, where $D(G)$ is the degree diagonal matrix and $A(G)$ is the adjacency matrix. The $\\alpha$-spectral radius of $G$ is the largest eigenvalue of $A_{\\alpha}(G)$. We give upper bounds for $\\alpha$-spectral radius for unicyclic graphs $G$ with maximum degree $\\Delta\\ge 2$, connected irregular graphs with given maximum degree and and some other graph parameters, and graphs with given domination number, respectively. We determine the unique"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.03456","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":""},"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"}