{"paper":{"title":"On the extremal total reciprocal edge-eccentricity of trees","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Lifang Zhao, Shuchao Li","submitted_at":"2015-08-24T03:32:37Z","abstract_excerpt":"The total reciprocal edge-eccentricity is a novel graph invariant with vast potential in structure activity/property relationships. This graph invariant displays high discriminating power with respect to both biological activity and physical properties. If $G=(V_G,E_G)$ is a simple connected graph, then the total reciprocal edge-eccentricity (REE) of $G$ is defined as $\\xi^{ee}(G)=\\sum_{uv\\in E_G}(1/\\varepsilon_G(u)+1/\\varepsilon_G(v))$, where $\\varepsilon_G(v)$ is the eccentricity of the vertex $v$. In this paper we first introduced four edge-grafting transformations to study the mathematical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.05690","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"}