{"paper":{"title":"Subtractive Magic and Antimagic Total Labeling for Basic Families of Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Inne Singgih","submitted_at":"2018-11-07T17:36:29Z","abstract_excerpt":"A \\textit{subtractive arc-magic labeling} (SAML) of a directed graph $G=(V,A)$ is a bijection $\\lambda :V\\cup A \\to \\{1,2,\\ldots,|V|+|A|\\}$ with the property that for every $xy\\in A$ we have $\\lambda(xy)+\\lambda(y)-\\lambda(x)$ equals to an integer constant. If $\\lambda(xy)+\\lambda(y)-\\lambda(x)$ are distinct for every $xy\\in A$, then $\\lambda$ is a \\textit{subtractive arc-antimagic labeling} (SAAL). A \\textit{subtractive vertex-magic labeling} (SVML) of $G$ is such bijection with the property that for every $x\\in V$ we have $\\lambda(x)+\\sum_{y\\in V, yx \\in A} \\lambda(yx)-\\sum_{y\\in V, xy\\in A}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03033","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"}