{"paper":{"title":"The $A_\\alpha$-spectral radius of graphs with given degree sequence","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dan Li, Jixiang Meng, Yuanyuan Chen","submitted_at":"2018-06-07T10:32:07Z","abstract_excerpt":"Let $G$ be a graph with adjacency matrix $A(G)$, and let $D(G)$ be the diagonal matrix of the degrees of $G$. For any real $\\alpha\\in[0,1]$, write $A_\\alpha(G)$ for the matrix $$A_\\alpha(G)=\\alpha D(G)+(1-\\alpha)A(G).$$ This paper presents some extremal results about the spectral radius $\\rho(A_\\alpha(G))$ of $A_\\alpha(G)$ that generalize previous results about $\\rho(A_0(G))$ and $\\rho(A_{\\frac{1}{2}}(G))$. In this paper, we give some results on graph perturbation for $A_\\alpha$-matrix with $\\alpha\\in [0,1)$. As applications, we characterize all extremal trees with the maximum $A_\\alpha$-spect"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.02603","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"}