{"paper":{"title":"The general spectral radius and majorization theorem of $t$-cone graphs with given degree sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Muhuo Liu, Yufei Huang","submitted_at":"2019-08-17T02:14:04Z","abstract_excerpt":"The general spectral radius of a graph $G$, denoted by $\\Theta(G,\\alpha)$, is the maximal eigenvalue of $M_{\\alpha}(G)=A(G)+\\alpha D(G)$ $(\\alpha\\geq 0)$, where $A(G)$ and $D(G)$ are the adjacency matrix and the diagonal matrix of vertex degrees of $G$, respectively. A graph $G$ is called $\\Theta_\\alpha$-maximal in a class of connected simple graphs $\\mathcal {G}$ if $\\Theta(G,\\alpha)$ is maximal among all graphs of $\\mathcal {G}$. A $t$-cone $c$-cyclic graph is the join of a complete graph $K_t$ and a $c$-cyclic connected simple graph. Let $\\pi=\\big(d_1,d_2,\\ldots,d_n\\big)$ and $\\pi'=\\big(d'_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.06224","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/1908.06224/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"}