{"paper":{"title":"Extremal values on the eccentric distance sum of trees","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Meng Zhang, Shuchao Li","submitted_at":"2012-06-30T12:15:17Z","abstract_excerpt":"Let $G=(V_G, E_G)$ be a simple connected graph. The eccentric distance sum of $G$ is defined as $\\xi^{d}(G) = \\sum_{v\\in V_G}\\varepsilon_{G}(v)D_{G}(v)$, where $\\varepsilon_G(v)$ is the eccentricity of the vertex $v$ and $D_G(v) = \\sum_{u\\in V_G}d_G(u,v)$ is the sum of all distances from the vertex $v$. In this paper the tree among $n$-vertex trees with domination number $\\gamma$ having the minimal eccentric distance sum is determined and the tree among $n$-vertex trees with domination number $\\gamma$ satisfying $n = k\\gamma$ having the maximal eccentric distance sum is identified, respectivel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0083","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"}