{"paper":{"title":"The matching energy of graphs with given edge connectivity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Hongping Ma, Shengjin Ji","submitted_at":"2014-05-07T13:34:42Z","abstract_excerpt":"Let G be a simple graph of order $n$ and $\\mu_1,\\mu_2,\\ldots,\\mu_n$ the roots of its matching polynomial. The matching energy of $G$ is defined as the sum $\\sum_{i=1}^n|\\mu_i|$. Let $K_{n-1,1}^k$ be the graph obtained from $K_1\\cup K_{n-1}$ by adding $k$ edges between $V(K_1)$ and $V(K_{n-1})$. In this paper, we show that $K_{n-1,1}^k$ has maximum matching energy among all connected graph with order $n$ and edge connectivity $k$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1601","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"}