{"paper":{"title":"Magic labelings of distance at most 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Alfan Sukmana Praja, Ira Apni Purwasih, Mohammad Navie Jauhari, Mona Elviyenti, Rinovia Simanjuntak","submitted_at":"2013-12-30T05:32:02Z","abstract_excerpt":"For an arbitrary set of distances $D\\subseteq \\{0,1, \\ldots, d\\}$, a graph $G$ is said to be $D$-distance magic if there exists a bijection $f:V\\rightarrow \\{1,2, \\ldots , v\\}$ and a constant {\\sf k} such that for any vertex $x$, $\\sum_{y\\in N_D(x)} f(y) ={\\sf k}$, where $N_D(x) = \\{y \\in V| d(x,y) \\in D\\}$.\n  In this paper we study some necessary or sufficient conditions for the existence of $D$-distance magic graphs, some of which are generalization of conditions for the existence of $\\{1\\}$-distance magic graphs. More specifically, we study $D$-distance magic labelings for cycles and $D$-di"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7633","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"}