{"paper":{"title":"New Bounds for the Sum of Powers of Normalized Laplacian Eigenvalues of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alessandra Cornaro, Gian Paolo Clemente","submitted_at":"2015-08-03T12:05:50Z","abstract_excerpt":"For a simple and connected graph, a new graph invariant $s_{\\alpha}^{*}(G)$, defined as the sum of powers of the eigenvalues of the normalized Laplacian matrix, has been introduced by Bozkurt and Bozkurt in [7]. Lower and upper bounds have been proposed by the authors. In this paper, we localize the eigenvalues of the normalized Laplacian matrix by adapting a theoretical method, proposed in Bianchi and Torriero ([5]), based on majorization techniques. Through this approach we derive upper and lower bounds of $s_{\\alpha}^{*}(G)$. Some numerical examples show how sharper results can be obtained "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.00386","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"}