{"paper":{"title":"Complete solution to a problem on the maximal energy of unicyclic bipartite 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":"2010-10-29T06:03:20Z","abstract_excerpt":"The energy of a simple graph $G$, denoted by $E(G)$, is defined as the sum of the absolute values of all eigenvalues of its adjacency matrix. Denote by $C_n$ the cycle, and $P_n^{6}$ the unicyclic graph obtained by connecting a vertex of $C_6$ with a leaf of $P_{n-6}$\\,. Caporossi et al. conjecture that the unicyclic graph with maximal energy is $P_n^6$ for $n=8,12,14$ and $n\\geq 16$. In``Y. Hou, I. Gutman and C. Woo, Unicyclic graphs with maximal energy, {\\it Linear Algebra Appl.} {\\bf 356}(2002), 27--36\", the authors proved that $E(P_n^6)$ is maximal within the class of the unicyclic biparti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.6129","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"}