{"paper":{"title":"Resolvent Energy of Unicyclic, Bicyclic and Tricyclic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Edin Glogi\\'c, Emir Zogi\\'c, Ivan Gutman, Juliane Capaverde, Luiz Emilio Allem, Vilmar Trevisan","submitted_at":"2015-12-30T13:28:10Z","abstract_excerpt":"The resolvent energy of a graph $G$ of order $n$ is defined as $ER=\\sum_{i=1}^n (n-\\lambda_i)^{-1}$, where $\\lambda_1,\\lambda_2,\\ldots,\\lambda_n$ are the eigenvalues of $G$. In a recent work [Gutman et al., {\\it MATCH Commun. Math. Comput. Chem.\\/} {\\bf 75} (2016) 279--290] the structure of the graphs extremal w.r.t. $ER$ were conjectured, based on an extensive computer--aided search. We now confirm the validity of some of these conjectures."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.08938","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"}