{"paper":{"title":"Cylindrical Grid Graphs $P_m \\Box C_n$ are Non-Distance Magic","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Julia K. Abraham, Sajidha P, V. Vilfred Kamalappan","submitted_at":"2023-03-18T14:41:02Z","abstract_excerpt":"A bijective mapping $f: V(G) \\rightarrow \\left\\{1,2,\\ldots,n\\right\\}$ is called a \\emph{Distance Magic Labeling (DML) of $G$} if ~ ${\\sum_{v \\in N(u)}} f(v) $ is a constant for all $u\\in V(G)$ where $G$ is a simple graph of order $n$ and $N(u)$ = $\\{v\\in V(G):$ $uv\\in E(G)\\}$. Graph $G$ is called a \\emph{Distance Magic Graph (DMG)} if it has a DML, otherwise it is called a \\emph{Non-Distance Magic (NDM) graph}. In 1996, Vilfred proposed a conjecture that cylindrical grid graphs $P_m \\Box C_n$ are NDM for $m \\geq 2$, $n \\geq 3$ and $m,n\\in\\mathbb{N}$. Recently, the authors could prove the conje"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.12222","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2303.12222/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}