{"paper":{"title":"On the k-edge magic graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Gee-Choon Lau, Saeid Alikhani, Sin-Min Lee, William Kocay","submitted_at":"2012-07-12T14:16:13Z","abstract_excerpt":"Let $G$ be a graph with vertex set V and edge set E such that |V| = p and |E| = q. For integers k\\geq 0, define an edge labeling f : E \\rightarrow \\{k,k+1,....,k+q-1\\} and define the vertex sum for a vertex $v$ as the sum of the labels of the edges incident to v. If such an edge labeling induces a vertex labeling in which every vertex has a constant vertex sum (mod p), then G is said to be k-edge magic (k-EM). In this paper, we (i) show that all the maximal outerplanar graphs of order p = 4; 5; 7 are k-EM if and only if k\\equiv 2 (mod p); (ii) obtain all the maximal outerplanar graphs that are"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.2977","kind":"arxiv","version":2},"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"}