{"paper":{"title":"Cube-magic labelings of grids","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Joe Ryan, Rachel Wulan Nirmalasari Wijaya, Thomas Kalinowski","submitted_at":"2017-02-08T22:22:40Z","abstract_excerpt":"We show that the vertices and edges of a $d$-dimensional grid graph $G=(V,E)$ ($d\\geqslant 2$) can be labeled with the integers from $\\{1,\\ldots,\\lvert V\\rvert\\}$ and $\\{1,\\ldots,\\lvert E\\rvert\\}$, respectively, in such a way that for every subgraph $H$ isomorphic to a $d$-cube the sum of all the labels of $H$ is the same. As a consequence, for every $d\\geqslant 2$, every $d$-dimensional grid graph is $Q_d$-supermagic where $Q_d$ is the $d$-cube."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.02639","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"}