{"paper":{"title":"On Distance Antimagic Graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Kristiana Wijaya, Rinovia Simanjuntak","submitted_at":"2013-12-28T08:22:19Z","abstract_excerpt":"For an arbitrary set of distances $D\\subseteq \\{0,1, \\ldots, diam(G)\\}$, a $D$-weight of a vertex $x$ in a graph $G$ under a vertex labeling $f:V\\rightarrow \\{1,2, \\ldots , v\\}$ is defined as $w_D(x)=\\sum_{y\\in N_D(x)} f(y)$, where $N_D(x) = \\{y \\in V| d(x,y) \\in D\\}$. A graph $G$ is said to be $D$-distance magic if all vertices has the same $D$-vertex-weight, it is said to be $D$-distance antimagic if all vertices have distinct $D$-vertex-weights, and it is called $(a,d)-D$-distance antimagic if the $D$-vertex-weights constitute an arithmetic progression with difference $d$ and starting value"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7405","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"}