{"paper":{"title":"Super edge-graceful paths","license":"http://creativecommons.org/licenses/by/3.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Dalibor Froncek, Sylwia Cichacz, Wenjie Xu","submitted_at":"2008-04-23T05:02:06Z","abstract_excerpt":"A graph $G(V,E)$ of order $|V|=p$ and size $|E|=q$ is called super edge-graceful if there is a bijection $f$ from $E$ to $\\{0,\\pm 1,\\pm 2,...,\\pm \\frac{q-1}{2}\\}$ when $q$ is odd and from $E$ to $\\{\\pm 1,\\pm 2,...,\\pm \\frac{q}{2}\\}$ when $q$ is even such that the induced vertex labeling $f^*$ defined by $f^*(x) = \\sum_{xy\\in E(G)}f(xy)$ over all edges $xy$ is a bijection from $V$ to $\\{0,\\pm 1,\\pm 2...,\\pm \\frac{p-1}{2}\\}$ when $p$ is odd and from $V$ to $\\{\\pm 1,\\pm 2,...,\\pm \\frac{p}{2}\\}$ when $p$ is even. \\indent We prove that all paths $P_n$ except $P_2$ and $P_4$ are super edge-graceful."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.3640","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"}