{"paper":{"title":"Super edge-magic deficiency of join-product graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"A.A.G. Ngurah, Rinovia Simanjuntak","submitted_at":"2014-01-18T08:15:14Z","abstract_excerpt":"A graph $G$ is called \\textit{super edge-magic} if there exists a bijective function $f$ from $V(G) \\cup E(G)$ to $\\{1, 2, \\ldots, |V(G) \\cup E(G)|\\}$ such that $f(V(G)) = \\{1, 2, \\ldots, |V(G)|\\}$ and $f(x) + f(xy) + f(y)$ is a constant $k$ for every edge $xy$ of $G$. Furthermore, the \\textit{super edge-magic deficiency} of a graph $G$ is either the minimum nonnegative integer $n$ such that $G \\cup nK_1$ is super edge-magic or $+\\infty$ if there exists no such integer.\n  \\emph{Join product} of two graphs is their graph union with additional edges that connect all vertices of the first graph t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.4522","kind":"arxiv","version":2},"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"}