{"paper":{"title":"Matching Energy of Unicyclic and Bicyclic Graphs with a Given Diameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Jinfeng Liu, Lin Chen, Yongtang Shi","submitted_at":"2014-09-06T17:51:57Z","abstract_excerpt":"Gutman and Wagner proposed the concept of matching energy (ME) and pointed out that the chemical applications of ME go back to the 1970s. Let $G$ be a simple graph of order $n$ and $\\mu_1,\\mu_2,\\ldots,\\mu_n$ be the roots of its matching polynomial. The matching energy of $G$ is defined to be the sum of the absolute values of $\\mu_{i}\\ (i=1,2,\\ldots,n)$. In this paper, we characterize the graphs with minimal matching energy among all unicyclic and bicyclic graphs with a given diameter $d$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2039","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"}