{"paper":{"title":"Complete solution to a conjecture on the maximal energy of unicyclic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Bofeng Huo, Xueliang Li, Yongtang Shi","submitted_at":"2010-11-21T12:25:51Z","abstract_excerpt":"For a given simple graph $G$, the energy of $G$, denoted by $E(G)$, is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix. Let $P_n^{\\ell}$ be the unicyclic graph obtained by connecting a vertex of $C_\\ell$ with a leaf of $P_{n-\\ell}$\\,. In [G. Caporossi, D. Cvetkovi\\'c, I. Gutman, P. Hansen, Variable neighborhood search for extremal graphs. 2. Finding graphs with extremal energy, {\\it J. Chem. Inf. Comput. Sci.} {\\bf 39}(1999) 984--996], Caporossi et al. conjectured that the unicyclic graph with maximal energy is $C_n$ if $n\\leq 7$ and $n=9,10,11,13,15$\\,, an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.4658","kind":"arxiv","version":2},"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"}